Question

Item 4 Identify the initial amount $a$ and the rate of growth $r$ (as a percent) of the exponential function $y=12\left(1.05\right)^t$ . Evaluate the function when $t=5$ . Round your answer to the nearest tenth.

Answer 1

Initial amount = 12

Rate of growth = 5%

value of the function when t t = 5 is 15.3

Explanation:

The standard exponential growth equation is expressed as;

y = A(1+r)^t

A is the initial amount

r is the rate of growth

t is the time

Given the expression y = 12(1.05)^t

On comparing with the general formula;

A = 12

Hence the initial amount is 12

Also;

1 + r = 1.05

r = 1.05 -1

r = 0.05

r = 0.05 * 100

r = 5%

The rate of growth is 5%

To evaluate the function when t = 5, we will substitute t = 5 into the given function as shown;

Recall that y = A(1+r)^t

y = 12(1.05)^5

y = 12(1.2763)

y = 15.3 (to the nearest tenth)