A bacterial culture starts with 400 bacteria and grows at a rate proportional to its size. After 2 hours there will be 800 bacteria.
1) Express the population, P(t) after t hours as a function of t
2) Using your equation from above, what will the population be after 8 hours?
3) Using your equation from above, after how many hours will the population reach 2270 bacteria?

Answers

Answer 1

Answer:

P(t) = 400×2^(t/2)64005.0

Step-by-step explanation:

The wording "a rate proportional to its size" is an indication that growth (or decay) is exponential.

1) For many problems involving exponential growth, I like to use the numbers given in the problem statement as follows.

  population = (initial population) × (growth factor)^(t/(growth period))

where the "growth period" is the period of time in which the population is multiplied by the "growth factor".

Here, we're given ...

  (initial population) = 400

  (growth factor) = 800/400 = 2

  (growth period) = 2 . . . . hours

So, our population function can be written as ...

  P(t) = 400×2^(t/2)

__

2) Putting t=8 into the formula, we get ...

  P(8) = 400×2^(8/2) = 400×16 = 6400

After 8 hours, the population will be 6400.

__

3) Fill in the given number and solve for t.

  2270 = 400×2^(t/2)

  2270/400 = 2^(t/2)

Taking logs, we have ...

  log(227/40) = (t/2)log(2)

  t = 2×log(227/40)/log(2) ≈ 5.009

After 5.0 hours, the population will reach 2270.


Related Questions


Will mark brainlist

Given. QR I PT and Prove: APQR – ATSR
Angles
Segments
Triangles Statements Reasons
ZQPR
ZQRP

Answers

Final answer:

The mathematics question involves proving two triangles congruent in geometry, likely using congruence criteria such as SSS, SAS, or ASA, with the given information that line QR is parallel to PT.

Explanation:

The subject of this question is Mathematics, specifically it involves geometry and the proof of congruent triangles. The statement 'QR I PT' suggests that line QR is parallel to line PT. To prove triangles APQR and ATSR are congruent, one would need to demonstrate that they satisfy the criteria for congruence such as side-side-side (SSS), side-angle-side (SAS), or angle-side-angle (ASA). The angles mentioned, such as ∠QPR and ∠QRP, are likely parts of the required congruence criteria. However, additional information and a specific criteria of congruence need to be applied in a step-by-step explanation.

Using the rule of 72, how long will it take for the principal to double with an annual compound interest rate of 6%?
A. 6
B. 9
C. 12
D. 15

Answers

Answer:

C. 12

Step-by-step explanation:

With the rule of 72, you would divide 72 by the periodic interest rate to get the number of years for the principal to double

72 ÷ 6 = 12

Which two-dimensional figure results from slicing the sphere with the blue plane?

A square

A circle

A line

A cone

A parabola

Answers

The answer is A parabola

What is the 30th term of the linear sequence below?

5
,

7
,

9
,

11
,

13
,
.
.
.

Answers

Answer:

63

Step-by-step explanation:

5,7,9,11,13

common factor= adding by 2

2n+3

find the 30th term

2×30+3=63

answer= 63

Final answer:

The 30th term of the linear sequence −5, −7, −9, −11, −13, . . . is -63. This is found using the formula for the nth term of a linear sequence, which is expressed as nth term = first term + (n - 1)*common difference.

Explanation:

The 30th term of a linear sequence can be found using the formula: nth term = first term + (n - 1)*common difference. In this sequence, the first term is -5 and the common difference (distance between each term) is -2 (since -7 minus -5 equals -2).

By substituting the appropriate values into the formula, we get: 30th term = -5 + (30 - 1)*(-2) = -5 - 58 = -63. Therefore, the 30th term of the sequence is -63.

Learn more about Linear Sequence here:

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The measure of central angle RST is pi radians. What is the area of the shaded sector? 4pi units^2 8pi units^2 16pi units^2 20pi units^2

Answers

Answer:

8π units²

Step-by-step explanation:

Area of the circle can be defined as pi 'π' times  the radius squared 'r²'

A= πr²

radius given is 4 (see attachment for the figure)

r=4

A = π4²

A= 16π

Now, if you look at the figure, you can see that the shaded area of the circle is 'half' of the whole circle.

We will half the Area which we have found it above in order to determine the area of shaded sector

Therefore,

area of the shaded sector =  16π/2 => 8π units²

Answer:

8[tex]\pi[/tex] [tex]units^{2}[/tex]

Step-by-step explanation:

did it on edge

Nicole sells T-shirts, t, for $8, and sells sweatshirts, s, for $18. She earns $475
in revenue. Which equation below represents this relationship?

Answers

Answer:

Step-by-step explanation:

Cost of t, T-shirts = t*8  = 8t

Cost of s, sweatshirts = s*18 = 18s

Equation:

8t + 18s = 475

Which of the following is a prime number? 99, 53, 117, 121

Answers

53 is a prime number

Answer:

53

Step-by-step explanation:

99 can be divisible by 9, 11, 3, and 33. 117 can be divisible by 11 (11x11)

and 117 can be divisible by 1, 3, 9, 13, and 39.

What is the average rate of change for f(x) = -3* + 1 over the interval -2 < x <-1?
A. -1/9. B. -2/9. c. 1/9. d. 2/9

Answers

Answer:

B

Step-by-step explanation:

You can check it before choosing the answer.

I think 85% correct.

Find the value of x in the triangle

Answers

Answer:

x = 28

Step-by-step explanation:

The sum of the angles of a triangle add to 180

85+67+x = 180

Combine like terms

152 +x =180

Subtract 152 from each side

152-152+x = 180-152

x = 28

Answer:

x=28 degrees

Step-by-step explanation:

180-85=95

95-67=28


The ratio of dogs to cats at the local pet store is 5:3
If there is 12 cats at the pet store, how many dogs
are at the pet store?

Answers

Answer:

20 dogs

Step-by-step explanation:

Answer:

20 Dogs.

Step-by-step explanation:

5:3=x:12

12/3=4

5x4=20

) Yoona gives guitar lessons for $70 per session. She gives a 10% discount to students who
come to her studio for the lesson.

Answers

Final answer:

The question is about calculating the price of guitar lessons after a 10% discount and the answer explains the steps to calculate the discounted price.

Explanation:

The subject of this question is Mathematics and the grade level is High School.

To calculate the amount after the discount, subtract 10% of $70 from $70. 10% of $70 is $7, so the discounted price is $70 - $7 = $63.

Therefore, Yoona gives a 10% discount to students which means the price per session is $63.

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Janine walks on a circular track whose radius is 60 meters. If she walks a total of 100 meters, which of the following represents the radian angle she rotates about the center of the track?
(1) 5/3
(2) 3/5
(3) 5π/3
(4) 3π/5

Answers

Answer: OPTION 1

Step-by-step explanation:

For this exercise you need to remember that, by definition, the Arc length can be calculated with the following formula:

[tex]arc\ length=rC[/tex]

where "C" is the central angle of the arc in radians and "r" is the radius.

Since you need to find the Central  angle, you have to solve for "C" from that formula, as following:

[tex]C=\frac{arc\ length}{r}[/tex]

According to the information given in the exercise, you can identify that:

[tex]arc\ length=100\ m\\\\r=60\ m[/tex]

Therefore, the final step is to substitute these values into the formula and evaluate, in order to find the value of "C":

[tex]C=\frac{100\ m}{60\ m} \\\\C=\frac{5}{3}\ rad[/tex]

What method can we use to rewrite Quadratic Equation in standard form to a Quadratic Formula? Go ahead and rewrite ax^2 + bx+c = 0 to quadratic formula. (please help. this is urgent.)

Answers

Answer:

SOLUTION: Rewrite the quadratic equation in standard form by completing the square. f(x)=x^2+8x+14 Answer (f(x)= (x, plus or minus ___)^2 plus or minus ____ I have worked this to x, 4 a Algebra -> Quadratic Equations and Parabolas -> SOLUTION: Rewrite the quadratic equation in standard form by completing the square.

Step-by-step explanation:

A jar contains 2 caramels, 7 mints and 16
dark chocolates. What is the probability of
choosing a dark chocolate, eating it, then
choosing a caramel?

Answers

the answerrrrrr is: 16:25 ratio wise

Answer:

Answer A: 16/25

Answer B: 2/24

Step-by-step explanation:

There are 16 dark chocolates, so the probability of choosing one is 16/25. the total number of candies is 25, so when one  is eaten, the number changes to 24. There are 2 caramels, so the number is 2/24.

Does the following list represent a complete probability model? Explain.
P(red) = 16 , P(yellow) = 13 , P(blue) = 112 , and P(green) = 12

Answers

Answer:

No

Step-by-step explanation:

No, the given list does not represent a complete probability model because the sum of the probabilities is not equal to 1.

The sum of probabilities should always equal to 1 in a complete probability model. In this case, the sum of probabilities is 16 + 13 + 112 + 12 = 153, which is not equal to 1. Therefore, it is not a complete probability model.

Final answer:

The provided list does not form a complete probability model because the probabilities do not sum up to 1, and some values exceed 1, which is not possible for probabilities.

Explanation:

The list provided does not represent a complete probability model because the probabilities of all possible outcomes of a probability model must sum up to 1. However, the sum of the probabilities listed (P(red) = 16, P(yellow) = 13, P(blue) = 1/12, and P(green) = 1/2) does not equal 1. The values for P(red) and P(yellow) seem to be mistakes or typos, as probabilities cannot be greater than 1. If these values were supposed to represent fractions and perhaps there are typos, they may need correcting to ensure the probabilities would sum up to 1. An example of a complete probability model can be seen in the jelly bean question mentioned, where the probabilities of selecting each color are fractions that sum up to 1.

is x greater than, less than, or equal to 50*

Answers

Answer:

c

Step-by-step explanation:

because they are opposites

I think > 50 since the x angle is bigger. I believe it’s not verticle angle

mathhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh

Answers

Answer:

21

Step-by-step explanation:

2³ = 8

8/2

= 4

3.4(5)

= 17

4 + 17

= 21

Answer:

Your answer is going to be: 21.

Step-by-step explanation:

In this problem, we're going to be using PEMDAS.

[tex]\frac{1}{2} x^{3} +3.4y[/tex]

Now, we have to fill the blanks:

[tex]\frac{1}{2} 2^{3} +3.45[/tex] [tex](5)\\[/tex]

There's no parenthesis (3.45(5) is just another way of multiplying so that doesn't count). So, we move to the exponent part.

[tex]\frac{1}{2} 8+3.4(5)[/tex]

Everything else is just multiplication.

[tex]\frac{8}{2} + 17[/tex] = 4+ 17

Add it all together and your answer is going to be:

21.

P.S. Good luck with the rest of your assignment!!

uuuuLITUNCION
Given the function f(x) = -2x2 + 3 over the closed
interval [-1, 2], what are the extreme values?
Minimum:
Maximum:

Answers

Answer:

Step-by-step explanation:

hello :

f(x) = -2x²+3

in : [-1, 2]   f'(x) = - 4x

f'(x) = 0  means : -4x=0   so : x=0

f(0) = -2(0)²+3 = 3 (Maximum:) because : a= -2 and a<0

in :  [-1, 0]   f is  crasing

in :  [-1, 2]   f is  decrasing

Answer:

1.-5

2.3

Step-by-step explanation:

just did it

(x + 3)2 + (x + 3) - 2 = 0​

Answers

Answer:

x=-7/3

Step-by-step explanation:

2(x+3)+(x+3)-2=0

2x+6+x+3-2=0

3x+7=0

3x=-7

x=-7/3

Answer:

Step-by-step explanation:

RE-POST --> BRAINLIEST, THANKS, 5-STAR RATING IF YOU ANSWER! PLEASE HURRY!

Nini's (me) grade average in Science is a 96.7%. She has a project that is due that is worth 10% of her grade. If she gets a 0% on the project, what is her new grade average?

This actually very important that I know immediately, so please answer soon!

Answers

Answer:

93.76%

Step-by-step explanation:

93.76% should be your new grade

I'm not 100% sure but what I did is that I divided each percent you have by it's worth. So for example, 96% x 20% = 0.192

I did this with all the possible percents and then I made them into whole number. So the 0.192 became 192. Here I divided it by 5. I should've divided by 4 but since the project is a 0% I didn't have to add it, just use it to divide.

So here I had 117.2 then I multiplied it by 80% because that's the total percent all those grades equaled and got 93.76%


Solve -4x ≥ -8. Graph the solution.

Answers

Answer: x is less then or equal to 2

Step-by-step explanation:

divide -4x and -8 both by -4 to get x is greater then or equal to 2 and flip the sign to less then or equal then because your dividing by a negative number

Find the common difference Ce:-34,-29,-24,-19,...

Answers

Answer:

d = 5

Step-by-step explanation:

The common difference d is the difference between consecutive terms in the sequence

- 29 - (- 34) = - 29 + 34 = 5

- 24 - (- 29) = - 24 + 29 = 5

- 19 - (- 24) = - 19 + 24 = 4

Thus the common difference is d = 5

Final answer:

The common difference between consecutive terms in the given sequence is 5.

Explanation:

The given sequence is {-34, -29, -24, -19, ...}

To find the common difference, we need to look for a pattern between consecutive terms. So, let's observe the differences between consecutive terms:

-29 - (-34) = 5

-24 - (-29) = 5

-19 - (-24) = 5

As we can see, the common difference between consecutive terms is 5.

A square's diagonal (hypotenuse) is 28V2. What is the length of each side?

Answers

In a square, all four sides are the same length. Imagine a square that has been cut by a diagonal. We have two triangles, each with the same length hypotenuse (diagonal length) and two equal side lengths. To find the length of each side, we can use the Pythagorean theorem.

I used x in place of a and b, as both side lengths are equal.

x^2 + x^2 = (28 [tex]\sqrt{2}[/tex])^2

2x^2 = 1568

x^2 = 784

x = 28

The length of each side is 28 units.

Hope this helps!! :)

Answer:

Once it is a square, the lengths are the same. Considering that

a square's diagonal is [tex]s\sqrt{2}[/tex], thus, each length measures 28.

You may use the pythagorean theorem:

[tex](28\sqrt{2} )^2=s^2+s^2\\28\sqrt{2} =\sqrt{s^2+s^2} \\28\sqrt{2} =s\sqrt{2} \\[/tex]

If ↔w||↔v, find the measurement of angle b.
∠b =

Answers

Answer:

∠ b = 132°

Step-by-step explanation:

Since v and w are parallel.

The angle vertically opposite 48° is congruent , thus = 48°

b and 48° are same- side interior angles and supplementary, thus

b = 180° - 48° = 132°

the midpoint of AB is M (6,3). If the coordinates of A are (7,4) what are the coordinates of B

Answers

Answer:

B(5,2)

Step-by-step explanation:

110/12 = 55/z
a.6
b.8
c.10
d.400

Answers

6 because 110/55=2 then divide 12 by 2 you get 6

Answer:

a. 6

Step-by-step explanation:

110/12 = 55/z

z = 55 × 12/110

z = 6

Solve the system of equations by substitution.
x+y=18
y=8x

Answers

Answer:

x=2, y=16

Step-by-step explanation:

x+y=18

y=8x

x+8x=18

x=2

y=16

Answer:

2

Step-by-step explanation:

x + y = 18

y = 8x

x + 8x = 18

9x = 18

x = 18÷9

x = 2

Evaluate each expression if a=4, b=6 and c=3
7c+8a-5b

Answers

Answer: 38

Step-by-step explanation:

To solve this problem, you are simply going to plug in the values for the numbers into the equation so it would look like this:

7(3)+8(4)-5(6)

Answer:

23

Step-by-step explanation:

7(3)+8(4)-5(6)

21+32-30

53-30

23

Oil prices are projected to increase by 100% by next june. A quart of oil currently costs $2.45. What is the projected cost of a gallon of oil next june?

Answers

Answer:

The projected cost of a gallon of oil by next june is $19.60.

Step-by-step explanation:

Given:

Oil prices are projected to increase by 100% by next june.

A quart of oil currently costs $2.45.

Now, to find the cost of a gallon of oil next june.

So, to get the projected cost of a quart of oil by next june:

Cost of one quart of oil currently = $2.45.

Rate of oil prices projected to increase by = 100%.

[tex]100\%\ of\ \$2.45+\$2.45\\\\=\frac{100}{100}\times 2.45+2.45\\\\=2.45+2.45\\\\=\$4.90.[/tex]

Now, to get the projected cost of a gallon of oil by next june we use conversion factor:

4 quart = 1 gallon.

If, 1 quart oil price = $4.90.

Then, 4 quarts oil price = [tex]\$4.90\times 4[/tex] = [tex]\$19.60.[/tex]

Thus, 1 gallon oil price = $19.60.

Therefore, the projected cost of a gallon of oil by next june is $19.60.

Answer:

19.60

Step-by-step explanation:

use the pythagorean theorem to prove whether or not each set of numbers represent the side length of a right triangle in your final answer, include your proof A. 6,12,15 B. 5,,12, and 13

Answers

Answer:

a. no, it is not a right triangle

b.  yes, it is a right triangle

Step-by-step explanation:

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