I need the answer and step by step on how to solve.

Question

Objective 3.4 - Evaluate Exponential

The hourly wage of some automobile plan workers went from $7.107.10 to $11.4011.40 in 7 years (annual raises).

If their wages are growing exponentially what will be their hourly wage in 9 more years?

Round to (nearest $0.10)

Answer 1

To solve this problem, we need to use the formula for exponential growth:

A = P(1 + r)^t

Where A is the final amount, P is the initial amount, r is the annual growth rate, and t is the number of years.

First, we need to find the annual growth rate. We can use the following formula:

r = (A/P)^(1/t) - 1

Plugging in the given values, we get:

r = (11.40/7.10)^(1/7) - 1

r ≈ 0.0621

Now we can use the formula for exponential growth to find the hourly wage in 9 more years:

A = 11.40(1 + 0.0621)^9

A ≈ 21.20

Rounding to the nearest $0.10, we get the final answer of $21.20 per hour.

Answer 2

11.40 = 7.10(r)⁶

1.605633803 = r⁶

1.069985942 = r

A(9) = 11.40(1.069985942)⁹

Can you calculate and answer?