The amount of money in an account may increase due to rising stock prices and decrease due to falling stock prices. Mason 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) = 10,125(1.83)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) 9,638 18,794.10 36,648.50 71,464.58
Which account recorded a greater percentage change in amount of money over the previous year? Justify your answer.
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Answer:
fThe 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(×), in dollars, in account A after x years is represented by the function below:
f(×)= 1264(1.09)^×
Part A: is the amount of money in account A increasing or decreasing and by what percentage per year? Justify your answer
Part B: The table below show the amount g(r), in dollars, of money in account B after r years:
(*see screen shot of table)
Which account recorded a greater percentage change in amount of money over the previous year? justify your answer.
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Expert Answer
Solution: Given, f(x) = 1264 (1.09)^x f(x) can be written as: f(x) = 1264 ( 1 + 0.09)^x f(x) = 1264 [ 1 + (9/100)]^x f(x) = 1264 ( 1 + 9%)^x The above expression for f(x) denotes the amount in account
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