Answer:
Thank you for your question. The worker’s contract states that the hourly wage will start at $10.50 and will increase by r = 4.5% annually, with the raise given every 12 months. This means that the worker’s hourly wage follows an exponential growth pattern, where the initial amount is a = $10.50, the growth rate is r = 0.045, and the number of time intervals passed is x = the number of years. To find the worker’s hourly wage after x years, we can use the exponential growth formula:
y = a (1 + r) x
where y is the amount after x time.
For example, if we want to find the worker’s hourly wage after 3 years, we can plug in x = 3 and get:
y = 10.50 (1 + 0.045) ^3 y = 10.50 (1.045) ^3 y = 10.50 (1.1407) y = $11.98
Therefore, the worker’s hourly wage after 3 years will be $11.98.
You can use this formula to calculate the worker’s hourly wage for any number of years, as long as the contract terms remain the same. I hope this helps you understand how to use the exponential growth formula.