The problem provides an equation $W(t) = 15 \cdot (1.03)^t$ that represents the hourly wages of an employee at Jimmy John's, where $t$ is the number of years the employee has worked. We need to find the hourly wage when the employee starts working (when $t=0$) and after working for 5 years (when $t=5$).

1. Problem Description

The problem provides an equation $W(t) = 15 \cdot (1.03)^t$ that represents the hourly wages of an employee at Jimmy John's, where $t$ is the number of years the employee has worked. We need to find the hourly wage when the employee starts working (when $t=0$) and after working for 5 years (when $t=5$).

2. Solution Steps

a) To find the hourly wage when the employee starts working, we need to find the value of $W(t)$ when $t=0$. Substitute $t=0$ into the equation:

$W(0) = 15 \cdot (1.03)^0$

Since any number raised to the power of 0 is 1, we have:

$W(0) = 15 \cdot 1$

$W(0) = 15$

b) To find the hourly wage after working for 5 years, we need to find the value of $W(t)$ when $t=5$. Substitute $t=5$ into the equation:

$W(5) = 15 \cdot (1.03)^5$

$W(5) = 15 \cdot (1.1592740743)$

$W(5) \approx 17.3891111145$

Rounding to two decimal places, we get $W(5) \approx 17.39$.

3. Final Answer

a) An employee would earn $15 when they start working.

b) An employee would earn approximately $17.39 after working there for 5 years.