Solution
a)
To find the exponential growth function, we apply the exponential growth formula which is
Where
Given that
Substitute the variables into the exponential growth formula
![\begin{gathered} 25100=23900(1+k)^5 \\ \text{Divide both sides by 23,900} \\ \frac{25100}{23900}=\frac{23900(1+k)^5}{23900} \\ 1.05021=(1+k)^5^{} \\ \sqrt[5]{1.05021}=1+k \\ 1.00984=1+k \\ \text{Collect like terms} \\ k=1.00984-1 \\ k=0.00984 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%2025100%3D23900%281%2Bk%29%5E5%20%5C%5C%20%5Ctext%7BDivide%20both%20sides%20by%2023%2C900%7D%20%5C%5C%20%5Cfrac%7B25100%7D%7B23900%7D%3D%5Cfrac%7B23900%281%2Bk%29%5E5%7D%7B23900%7D%20%5C%5C%201.05021%3D%281%2Bk%29%5E5%5E%7B%7D%20%5C%5C%20%5Csqrt%5B5%5D%7B1.05021%7D%3D1%2Bk%20%5C%5C%201.00984%3D1%2Bk%20%5C%5C%20%5Ctext%7BCollect%20like%20terms%7D%20%5C%5C%20k%3D1.00984-1%20%5C%5C%20k%3D0.00984%20%5Cend%7Bgathered%7D)
Hence, the exponential growth function is
Hence, the exponential growth function is
b)
For the population of the city in 2022,
Substitute for t into the exponential growth function
Hence, the population is 2022 is 27700 (nearest hundred)
The total amount of money Levi spent on renting movie and buying candy is $5.75
<h3>Equation</h3>
- Amount Levi rented movie = $3.20
- A package of candy = $2.55
Total = Amount Levi rented movie + A package of candy
= $3.20 + $2.55
= $5.75
Therefore, the total money spent by Levi is $5.75
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9514 1404 393
Answer:
11
Step-by-step explanation:
The degree of the given monomial is the sum of the exponents of the variables.
m has degree 6
n has degree 5
The degree of the monomial is 6+5 = 11.
Answer:
V = (1/3)πr²h
Step-by-step explanation:
The volume of a cone is 1/3 the volume of a cylinder with the same radius and height.
Cylinder Volume = πr²h
Cone Volume = (1/3)πr²h
where r is the radius (of the base), and h is the height perpendicular to the circular base.
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<em>Comment on area and volume in general</em>
You will note the presence of the factor πr² in these formulas. This is the area of the circular base of the object. That is, the volume is the product of the area of the base and the height. In general terms, ...
V = Bh . . . . . for an object with congruent parallel "bases"
V = (1/3)Bh . . . . . for a pointed object with base area B.
This is the case for any cylinder or prism, even if the parallel bases are not aligned with each other. (That is, it works for oblique prisms, too.)
Note that the cone, a pointed version of a cylinder, has 1/3 the volume. This is true also of any pointed objects in which the horizontal dimensions are proportional to the vertical dimensions*. (That is, this formula (1/3Bh), works for any right- or oblique pyramid-like object.)
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* in this discussion, we have assumed the base is in a horizontal plane, and the height is measured vertically from that plane. Of course, any orientation is possible.
To graph the equation, plot a few points then connect then with a line.
f(x) = 440 - 55x
Plug in numbers for x to get the y value.
f(0) = 440
f(1) = 385
f(2) = 330
f(3) = 275
f(4) = 220
f(5) = 165
So when you graph these points, the y intercept is y = 440 because the graph crosses the y axis at (0, 440).
The x intercept is where the graph crosses the x axis. This happens when y = 0.
0 = 440 - 55x. Solve for x.
55x = 440
x = 8
So the x intercept is x = 8
