Question

Can someone check my algebra homework regarding exponential growth?

The population of a town was 7652 in 2016. The population grows at a rate of 1.6% annually.

a.) use the exponential growth model to write an equation that estimates the population t years after 2016.

My work:
y = a (1 + r) ^t
y = 7652 ( 1 + 0.016 ) ^t
y = 7652 (1.016) ^t
y = 774.43^t

Firstly, I'm not sure I used the correct formula. I found a ton of different ones all regrding exponential growth so I decided to go with the one we previously used. Other than that, I'm a bit confused on if I should leave the ^t as is or if I was supposed to substitute it with a number. Would anyone be willing to check this for me? Thanks in advance.

Answer 1

You did everything right. You leave "t" by itself because you don't have a given time frame. But I'll say you used the correct formula and showed your work well.