The population of a town was 6575 in 2012. The population grows at a rate of 1.7 % annually. ( a ) Use the exponential growth model to write an equation that estimates the population years after 2010.

(b) Estimate the population of the town in 2025. Show your work.

(a) For 2010, f(x) = 6357.024×(1 + 0.017)ˣ

(b)  f(25) = 8185.93

Step-by-step explanation:

The initial population of the town in 2012 = 6575

The population growth rate = 1.7%

The exponential growth model is f(x) = a(1 + r)ˣ

Where;

a = The initial value = 6575

r = The rate of growth = 1.7%

x = The number of years,

Therefore, we have;

In 2010, we have f(x) = 6575(1 + 0.017)⁻² ≈ 6357.024

Therefore, the equation becomes;

f(x) = 6357.024×(1 + 0.017)ˣ

(b) In 2025, we have;

x = 2025 - 2012 = 13 years

∴ f(x) = 6575(1 + 0.017)¹³ = 8185.93

answer: a) (0,0), (1,1), (2,8), and (3,27).

step-by-step explanation:

0^3=0

1^3=1

2^3=8

3^3=27

in effect, the exponential equation for this would me y=3^x. each x-coordinate cubed is giving the y coordinate, so a is your answer : )