Question

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.
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

The account that recorded a greater percentage change in amount of money over the previous year is year 4

Part A: Is the amount of money in account A increasing or decreasing?

The exponential function is given as:

f(x) = 9628 * (0.92)^x

An exponential function is represented as:

f(x) = ab^x

If b is less than 0, then the function is an increasing function.

So, the function f(x) = 9628 * (0.92)^x is a decreasing function.

The percentage of decrement is then calculated as:

r =1 - b

This gives

r = 1 - 0.92

Evaluate

r = 0.08

Express as percentage

r = 8%

Hence, the percentage of decrement is 8%

Part B: The account that recorded a greater percentage change in amount of money over the previous year

r  1 2 3 4

g(r) 8,972 8,074.80 7,267.32 6,540.59

As a general rule:

As the number of years increases, the percentage change increases

Hence, the account that recorded a greater percentage change in amount of money over the previous year is year 4

Read more about exponential functions at:

brainly.com/question/2456547

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