Write an exponential function. A population of 120,000 grows 1.2% per year for 15 years.

Question

jim_thompson5910 · Answer

The general form is 

$$\Large F = P(1+r)^{t}$$

F = final population (after t years)
P = initial population
r = growth rate (if negative, then you have exponential decay)
t = time in years

jim_thompson5910 · Answer

also, keep in mind that 1.2% = 0.012

mama2dylan · Answer

Thank you. Can you write the function out using the figures I provided @jim_thompson5910

jim_thompson5910 · Answer

You will plug in these values

P = 120000
r = 0.012
t = 15

and when you use a calculator, you can compute the value of F (the final population after t = 15 years)

jim_thompson5910 · Answer

so this basically

$$\Large F = P(1+r)^{t}$$

$$\Large F = 120000(1+0.012)^{15}$$

$$\Large F =\  ???$$

jim_thompson5910 · Answer

it seems odd how they want a function, but they say t = 15. So maybe they want you to not replace t with 15 and just leave it as 

$$\Large F(t) = P(1+r)^{t}$$

$$\Large F(t) = 120000(1+0.012)^{t}$$

$$\Large F(t) = 120000(1.012)^{t}$$

but I'm not sure

perl · Answer

i think its saying that the exponential function's domain is from t =0 to t=15

perl · Answer

since it is growing 1.2% each year

perl · Answer

over an interval of 15 years