The amount of money in an account may increase due to rising stock prices and decrease due to falling stock prices. Marco is studying the change in the amount of money in two accounts, A and B, over time.

Question

The amount f(x), in dollars, in account A after x years is represented by the function below:

f(x) = 9,628(0.92)x

Part A: Is the amount of money in account A increasing or decreasing and by what percentage per year? Justify your answer. (5 points)

Part B: The table below shows the amount g(r), in dollars, of money in account B after r years:

r (number of years) 1 2 3 4
g(r) (amount in dollars) 8,972 8,074.80 7,267.32 6,540.59

Which account recorded a greater percentage change in amount of money over the previous year? Justify your answer. (5 points)

Answer 1

Part A:

Notice how 0.92<1, which means that the function is decaying at a rate of 8% per year. This means that the amount of money will decrease by 8% per year.

Part B:

Here, we see that the decay rate is 10% per year since each consecutive term is being multiplied by 90% which is 10% less than 100%. Thus, Part B's account experiences a greater percentage change in amount of money over the previous year than Part A's account of 8%.

Answer 2

Thank you so much!!! :)

Answer 3

Glad I could help!