Question

Identify the initial amount a and the rate of growth r (as a percent) of the exponential function y = 12(1.05)t. Evaluate the function when t = 5. Round your answer to nearest tenth.

Answer 1

Exponential function is in the form of :
`y =a(1+r)^x` .....[1]

where a is the initial amount and r is the growth rate and (1+r) is the growth factor.

Given the function:
`y = 12(1.05)^t`

On comparing with equation [1] we have;

Initial amount(a) = 12

1+r = 1.05

Subtract 1 from both sides we get;

`r = 0.05` or 5%

Growth (r) = 0.05 or 5%

Now, evaluate the function for t = 5 we have;

Substitute the value of t=5 in the given function we have;

`y = 12(1.05)^(5)`

`y = 12 \cdot 1.27628156 = 15.3153787`

Therefore, the value of function when t=5 to the nearest tenth is 15.3