Answer:
The exponential function is [tex]C(t)=y(b)^t\ Or\ C(t)=1800(1.15)^1[/tex]
Step-by-step explanation:
Given
[tex]t[/tex] be the number of hours.
[tex]y[/tex] number of bacteria cells.
And we know that an exponential function is [tex]C(t)=y(b)^t[/tex],where [tex]b[/tex] is a positive real number, and in which the argument [tex]t[/tex] occurs as an exponent
The petri dish has [tex]1800[/tex] bacteria cells we can say that [tex]y=1800[/tex]
In the equation as [tex]C[/tex] is function of time and [tex](t)[/tex] will vary as [tex]1,2,3[/tex] for respective hours.
To find the value of [tex]b[/tex] we have to understand that it is dependent on percent increase if there is increment of [tex]15\%[/tex] then [tex]b=1+15\%=1+\frac{15}{100}=1+0.15=1.15[/tex]
So the exponential function will be [tex]C(t)=y(b)^t[/tex] ,plugging the values it will be equivalent to [tex]C(t)=1800(1+0.15)^1[/tex]
Check:
[tex]15\% of 1800 =0.15\times 1800=270[/tex]
So in first hour the cells will increased by a quantity of [tex]270[/tex] cells.
The number of cells after an hour in the petri dish [tex]=(1800+270)=2070[/tex]
That can also be from the formula.
[tex]C(t)=1800(1.15)^1=2070[/tex]
So the exponential function is [tex]C(t)=y(b)^t\ Or\ C(t)=1800(1.15)^1[/tex]
[tex]y[/tex] will increase exponentially as the value of [tex]t[/tex] increase.
Final answer:
The exponential function to represent the growth of bacteria cells, y, after t hours with an initial amount of 1800 cells and a 15% hourly growth rate is y = 1800(1 + 0.15)^t.
Explanation:
To write an exponential function showing the relationship between the number of bacteria cells, y, and the time in hours, t, we begin by using the initial value of 1800 bacteria cells and apply a 15% increase each hour. The exponential growth formula is given by y = P(1 + r)^t, where P is the initial amount, r is the growth rate (expressed as a decimal), and t is the time.
Since the growth rate is 15%, we convert this to a decimal by dividing by 100, resulting in 0.15. The formula to model this bacterial growth would be y = 1800(1 + 0.15)^t. Therefore, for any given number of hours t, you can calculate the number of bacteria cells y.
Graph a line with a slope of 2/5 that contains the point (-2,4)
A graph of the line with slope 2/5 and passing through the point (-2, 4) is shown on the coordinate plane in the image below.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):
[tex]y - y_1 = m(x - x_1)[/tex]
Where:
x and y represent the data points.m represent the slope.At data point (-2, 4) and a slope of 2/5, an equation for this line can be calculated by using the point-slope form as follows:
[tex]y - y_1 = m(x - x_1)[/tex]
y - 4 = 2/5(x - (-2))
y - 4 = 2/5(x + 2)
y = 2/5(x) + 4/5 + 4
y = 2/5(x) + 24/5
Read more on point-slope here: brainly.com/question/24907633
#SPJ3
In which quadrant is the number -14-5i located on the complex plane?
Answer:lll(3) Quadrant lll
Step-by-step explanation:Quadrant 3 is the quadrant where the imaginary part of a number and the real part of a number are both negative and in this number they both are.
is y=5-2x and 4x+2y=10 a single solution
Answer:
X= 0
Step-by-step explanation:
[tex]3x - 7 = 3x + 1[/tex]
solve for x
Answer:
No Solution.
Step-by-step explanation:
3x-7=3x+1
3x-3x-7=1
0-7=1
-7=1
no solution
to visit the of the empire state building, a ticket cost $4.00 in 1999.in 2009 ,the price rose to 20.00. what was the percent change?
Answer:
Step-by-step explanation:
i think its 500%
but im not sure
because 20 divided by 4 = 5
and 5.0 = 500%
Answer:
The percent change is 400%
Explanation:
We know that percentage change is given by the
[tex]\frac{change in value}{absolute value of the original value} \times 100[/tex]
i.e we find the difference between the original value and current value and then divide it by original value and multiply the obtained value with 100.
a negative percentage change indicates increase in value.
so we get 4 - 20 = -16
[tex]\frac{-16}{4}[/tex] = -4
[tex]-4 \times[/tex] 100 = -400
hence there is an increase of 400% in the percentage which is the required percentage.
Gas mileage is the number of miles you can drive on a gallon of gasoline. A test of a new car results in 560 miles on 20 gallons of gas. How far could you drive on 50 gallons of gas? What is the car’s gas mileage?
Answer:
Gas mileage is the number of miles you can drive
Gas mileage is the number of miles you can drive on a gallon of gasoline. A test of a new car results in 600 miles on 20 gallons of gas.
Step-by-step explanation:
Plzzz give me brainllest
Are coplanar points in the same line?
Answer:
I am not sure what you mean by same line but a CO planar point have to both share the same plane so not necessarily the same ray or line segment but it has to be on the same plane
Step-by-step explanation:
24:8,39:13 equvilent
Answer:
24 : 8 ≡ 39 : 13
Step-by-step explanation:
We are given two proportion relation and we have to determine whether they are equivalent or not.
Now, the first proportion is 24 : 8
So, the simplified proportion will be 24 : 8 = 8 × 3 : 8 = 3 : 1
Again the second proportion is 39 : 13
So, the simplified proportion is 39 : 13 = 13 × 3 : 13 = 3 : 1
Therefore, the two given proportions are equivalent i.e. 24 : 8 ≡ 39 : 13. (Answer)
Solve the system of equations:
3x + 2y = 4
3x + 6y = -24
Answer:
y=-7
x=6
Step-by-step explanation:
If you subtract 3x from both equations, you get -4y=28, which means that y=-7. When you substitute it back in, you get the x-value of 6.
What is the quotient of the complex numbers below?
(5-5i) = (3-i)
Answer:
A. 2- i
Step-by-step explanation:
Answer:
2 + i
Step-by-step explanation:
Find the Slope and Y-Intercer
1) y = x+3
slope =
y-intercept =
What’s the slope
Answer:
slope is 1 and y-intercept is 3
Step-by-step explanation:
equation is in the format y=mx+c
c = y-intercept
m = slope
if there is no number in front of x it is assumed that 1 is in front of x
Answer:
The slope is 1 and the y-intercept is 3
Step-by-step explanation:
y = x+3 has the form y = mx + b. If we compare these two equations, it becomes readily apparent that m = 1 and b = 3.
The slope is 1 and the y-intercept is 3 (or (0, 3) )
Find the area of a circle with a circumference of 18.84 units
welp
Answer:
A=28.25 is the rounded form of the answer.
A = 28.245673384359 in^2
Answer:
Area: 28.25
Step-by-step explanation:
Area = Circumference^2
4 (pi)
18.84^2 = 354.9456
4(pi) = 12.5663706144
354.9456 ÷ 12.5663706144 = 28.2456733843
Rounded to the nearest hundreth, the 5 in the thousandths place converts the 4 in the hundreths place into 5.
The sum of 3 consecutive odd numbers is 183
Answer:
Step-by-step explanation:The sum of three consecutive odd numbers is 183. Find the numbers. 57; 59; 67 59; 61; 63 60; 61; 62 65; 67; 69.
How do u do this I’m lost
Answer:
A = 1/3b
Step-by-step explanation:
Divide each side by 12b to isolate the variable "a". This leaves a = 4/12b. This can be simplified to 1/3b.
Steps to solve:
12ab/12b = 4/12b (Divide 12/b to both sides)
a = 4/12b
a = 1/3b (Answer)
______
Best Regards,
Wolfyy :)
what is the slope of y=-5+4x
Answer:
the slope is 4
Step-by-step explanation:
y=mx+ c
m=4
c=-5
Answer:y intercept :5
Step-by-step explanation:
slope-4
Need help with this math problem
Answer:
[tex]x=16[/tex]
Lenght of the equal sides: [tex]71\ units[/tex]
Step-by-step explanation:
You can observe in the picture that the triangle have two angles that have equal measure; therefore, it is an Isosceles triangle.
By definition, Isosceles triangles have two equal angles and two equal sides.
Based on this, you can write the following equation:
[tex]9x-73=3x+23[/tex]
Solving for "x", you get this value:
[tex]9x-3x=23+73\\\\6x=96\\\\x=\frac{96}{6}\\\\x=16[/tex]
Finally, you can subsitute the value of "x" into any expression to find the lenght of the equal sides:
[tex]3(16)+23=71\ units[/tex]
Grant has 2/3
of ice cream in a bowl. He then removes two 1/6
cups of ice cream to share with his little br
amount of ice cream left in Grant's bowl?
Answer: 2/6 or 1/3
Step-by-step explanation:
2/3 = 4/6. 1 /6 Two times is 2/6 so by subtracting you should get 2/6 or 1/3
Work out the size of angle X.
Answer:
x = 70°
Step-by-step explanation:
The external angle of a triangle is equal to the sum of the 2 opposite interior angles.
120° is an external angle of the triangle, thus
x + 50 = 120 ( subtract 50 from both sides )
x = 70
Caden answered 84% of the questions on her science test correctly. If she answered 21 questions correctly, how many questions were on the test?
A
25
B
26
C
27
D
28
Marie will earn $15 per hour at a new job. During training, she will earn $10 per hour. What percent of Marie's regular rate will she earn during training?
Answer:
66.67%
Step-by-step explanation:
Marie's earnings at a new job : $15 per hour
Her earnings during training : $10 per hour
percentage of Marie's regular rate earned by her during training
= [tex]\frac{Her\ earnings\ during\ training}{Her earning\ at\ a\ new\ job}[/tex]×100
= [tex]\frac{10}{15}[/tex]×100
= [tex]\frac{200}{3}[/tex]
= 66.67%
∴percentage of Marie's regular rate earned by her during training = 66.67%
Final answer:
To find what percentage of Marie's regular rate she will earn during training, divide her training rate by her regular rate and multiply by 100%.
Explanation:
Marie will earn $10 per hour during training. Her regular rate is $15 per hour. To calculate what percentage of her regular rate she will earn during training, we use the formula: percentage = (training rate / regular rate) * 100%. Plugging in the values, we get (10 / 15) * 100% = 66.67%. Therefore, Marie will earn 66.67% of her regular rate during training.
h/2 + 3 = 3(h/4 - 1)
Answer:
h=24
Step-by-step explanation:
h/2+3=3(h/4-1)
h/2+3=3h/4-3
h/2-3h/4=-3-3
2h/4-3h/4=-6
-h/4=-6
-h=-6*4
-h=-24
h=24
What should the following rate be divided by to convert it to a unit rate?
6 inches
12 hours
Answer:
so if all of the awnsers are whole numbers it is going to be 12/12
Step-by-step explanation:
Answer:
12
Step-by-step explanation:
Unit rate is a rate that has 1 as denominator.
Given the rate: 6 inches / 12 hours, we have to divide numerator and denominator by 12 to transform the denominator in 1, as follows:
[tex]\frac{6}{12} = \frac{6/12}{12/12} =[/tex] 0.5 inches/hour
you and your friend are collecting seashells on the beach. You collect 20 more shells than your friend collects. Together, you and your friend have 92 seashells. How many seashells do each of you collect
You first add 92+20. You will get 112. So 112 seashells collected.
Solve for y. Then find the values of y that correspond
to the given values of x for the linear function.
7. y + 8x = -2 for x = 0, 1,2-2,
8. 12x + 3y = 15 for x = -1, 0, 1
y - 3x = 9 for x = -2,0, 2
10. 0.4y + 2x = 1.2 for x = -3,0,
7.
y + 8x = -2
f(x) = y = -8x - 2
f(0)=-2, f(1)=-10, f(2)=-18, f(-2)=14
8.
12x + 3y = 15
3y = -12x + 15
f(x) = y = -4x + 5
f(-1)=9, f(0)=5, f(1)=1
9.
y - 3x = 9
f(x) = y = 3x + 9
f(-2)=3, f(0)=9, f(2)=15
10.
0.4y + 2x = 1.2
4y + 20x = 12
4y = -20x + 12
f(x) = y = -5x + 3
f(-3) = 18, f(0)=3
You want to work out the distance you have travelled on your bike so far. In total, you have travelled 600 km. You believe that for every 5 km travelled, 2 km of that was on your bike. How far have you travelled on your bike?
Answer:240 km
Step-by-step explanation: 600 ÷5 = 120, 120 × 2 = 240 km
I think that's the answer I'm not sure but hope this helps ;)
Pick the expression that matches this description:
A trinomial with a leading coefficient of 3 and a constant term of -5
Choose 1 answer:
(Choice A)
3m^2-5
(Choice B)
3m^2-5m+1
(Choice C)
-5m^2+4m+3
(Choice D)
3m^2+m-5
Answer:
D. [tex]3m^2+m-5[/tex]
Step-by-step explanation:
A trinomial expression is a polynomial expression with three terms.
The term with the highest power of variable is called the leading term and the co-efficient of this term is called the leading co-efficient.
The alone number without any variable in the expression is called the constant.
Example of a trinomial:
[tex]5x^2+2x+4[/tex]
Leading co-efficient = 5
Constant = 4
A trinomial with a leading coefficient of 3 and a constant term of -5 from the given choices is:
D. [tex]3m^2+m-5[/tex]
Find the exact volume of a cone 6yd height 5yd base
Answer:
The exact volume of a cone is 10 yd³.
Step-by-step explanation:
Given:
Height of cone (h) is 6 yd and base (b) is 5 yd.
Now, to get the volume we need to find the radius.
So, to find radius we put the formula of base:
Let the radius be [tex]r[/tex]
Base=[tex]\pi r^2[/tex]
[tex]b=\pi\times r^{2}[/tex]
[tex]5=\pi\times r^{2}[/tex]
Dividing both sides by π and using square root on both the sides:
[tex]5\div \pi=(\pi \times r^{2}) \div \pi[/tex]
[tex]\frac{5}{\pi}=r^{2}[/tex]
[tex]\frac{5}{\pi}=r^{2}[/tex]
[tex]r^{2}=\frac{5}{\pi}-----1[/tex]
Now, putting the formula for getting the volume (v) of cone:
Volume = [tex]\pi r^2\frac{h}{3}[/tex]
[tex]v=\pi\times r^{2}\times \frac{6}{3}[/tex]
[tex]v=\pi\times r^{2}\times 2[/tex]
Substituting the value of [tex]r^2[/tex] from equation (1), we get:
[tex]v=\pi\times \frac{5}{\pi}\times 2[/tex]
[tex]v=10[/tex] yd³
Volume of cone is 10 yd³
Therefore, the exact volume of a cone is 10 yd³.
Fractions between -8/10 and -4 / 5
Answer:
They are equal.
Step-by-step explanation:
-4/5=-8/10
Food bill before tax: $40
Sales Tax: 8% Tip: 17%
Answer: $50.00
Step-by-step explanation:
Org. Price- $40.00
10% - $4.00
1% - $0.40
8% - $3.20
Tax - $3.20
10% + 8% - 1% = 17%
4.00 + 3.20 - 0.40 = 6.80
Tip - $6.80
$40.00 + $3.20 + $6.80 = $50.00
A local hamburger shop sold a combined total of 500 hamburgers and cheeseburgers on Tuesday. There were 50 fewer cheeseburgers sold than hamburgers.
How many hamburgers were sold on Tuesday?
Answer: 275
Step-by-step explanation:
Let the total number of hamburger be x and the total number of cheeseburgers be y. That is
x + y = 500 ................... equation 1
Since there were 50 fewer cheeseburgers sold than hamburgers, this means that the number of hamburgers sold is more than cheeseburgers by 50 , that is
x - y = 50 ............. equation 2
solving the resulting linear equation by substitution method;
From equation 2 , make x the subject of the formula , that is
x = 50 + y ................ equation 3
substitute equation 3 into equation 1 , we have
50 + y + y = 500
50 + 2y = 500
2y = 500 - 50
2y = 450
y = 450/2
y = 225
substitute y = 225 into equation 3 to find the value of x. we have
x = 50 + y
x = 50 + 225
x = 275
Therefore 275 hamburgers were sold