Question

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.

Spam = 20 answers report ​

Answer 1

Account A: Decrease at 8% per year

Account B: Decrease at 10.00% per year

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

f(x) = 10,125(1.83)x

Account B shows the greater percentage change

$\huge\boxed{\fcolorbox{red}{pink}{Step by step}}$

Part A: Percentage change from exponential formula

f(x) = 9628(0.92)*

The general Formula for an exponential function is

y = ab^x, where

b = The base of exponential function

If b < 1, we have an exponential decay function

f(x) decreases as x increases as

Account A is decreases each year.

We can rewrite the formula for an exponential decay function as:

y = a(1 - b)", where

1 - b = decay factor

b = the percentage change in decimal form

If we compared the to formulas, we find

0.92 = 1 - b

b = 1 - 0.92 = 0.08 = 8%

The account is decreasing at an annual rate of 8%. The account is decreasing at an annual rate of 10.00%

Account B recorded a greater percentage change in the amount of money over the previous year.

Answer 2

f(x) = 9628(0.92)*

The general Formula for an exponential function is

y = ab^x, where

b = The base of exponential function

If b < 1, we have an exponential decay function f(x) decreases as x increases as

Account A is decreases each year.

We can rewrite the formula for an exponential decay function as:

y = a(1 - b)", where

1 - b = decay factor

b = the percentage change in decimal form

If we compared the to formulas, we find,

0.92 = 1 - b

b = 1 - 0.92 = 0.08 = 8%

The account is decreasing at an annual rate of 8%. The account is decreasing at an annual rate of 10.00%

Account B recorded a greater percentage change in the amount of money over the previous year.