The problem provides the equation $W(t) = 17.50 \cdot (1.04)^t$, which models an employee's hourly wage at Starbucks, where $t$ is the number of years the employee has worked. a) We need to find the starting wage, which means finding $W(0)$. b) We need to determine the annual percentage increase in wages. c) We need to find the wage after 5 years, which means finding $W(5)$.

1. Problem Description

The problem provides the equation $W(t) = 17.50 \cdot (1.04)^t$, which models an employee's hourly wage at Starbucks, where $t$ is the number of years the employee has worked.

a) We need to find the starting wage, which means finding $W(0)$.

b) We need to determine the annual percentage increase in wages.

c) We need to find the wage after 5 years, which means finding $W(5)$.

2. Solution Steps

a) To find the starting wage, we plug in $t=0$ into the equation:

$W(0) = 17.50 \cdot (1.04)^0$

$W(0) = 17.50 \cdot 1$

$W(0) = 17.50$

b) The equation is in the form $W(t) = a(1+r)^t$, where $a$ is the initial value and $r$ is the rate of increase. In our case, $1+r = 1.04$, so $r = 1.04 - 1 = 0.04$.

To express this as a percentage, we multiply by 100: $0.04 \cdot 100 = 4\%$.

c) To find the wage after 5 years, we plug in $t=5$ into the equation:

$W(5) = 17.50 \cdot (1.04)^5$

$W(5) = 17.50 \cdot 1.2166529024$

$W(5) \approx 21.291425792$

Rounding to two decimal places, we get $W(5) \approx 21.29$.

3. Final Answer

a) The starting wage is $17.

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0. b) The hourly wage increases by 4% each year.

c) The hourly wage after 5 years is approximately $21.

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9.