Question

write an exponential formula of the form f (t)= a×b^t to represent the following situation. assume t is in years. The beginning population is 27, 000, decreasing by 3.5% annually. f(t)=__________​

Answer 1

`f(t)= 27000 * 0.965^t`

Explanation:

Given

`a = 27000` -- initial

`r = 3.5\%`

Required

The exponential equation

The exponential equation is

`y =ab^t`

Where

`b=1 -r`

We used minus, because the rate decreases..

So, we have:

`b=1 -3.5\%`

`b=1 -0.035`

`b=0.965`

So:

`y =ab^t`

`y = 27000 * 0.965^t`

Hence:

`f(t)= 27000 * 0.965^t`