Question

write an exponential formula of the form f (t)=a×b^t to represent the following situation. assume t is in years. an investment of $11,500 triples every 14 years. round your values to the three decimal places. f(t)=________​

Answer 1

`f(t) = 11500 * (3)^{(t)/(14)}`

Step-by-step explanation

Given

`a = 11500` -- initial

`b = 3` ---- every 14 years

Required

The exponential equation

The exponential equation is:

`y =ab^T`

First, calculate the yearly rate.

Triples every 14 years, implies that:

`b = 3` -- the rate

`T=(t)/(14)` ---- time

So:

`y =ab^t`

`y = 11500 * (3)^{(t)/(14)}`

Hence:

`f(t) = 11500 * (3)^{(t)/(14)}`