2.(04.05 MC) The amount of money in an account may increase due to rising stock prices and decrease due to falling stock prices. Emerson 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) = 1,264(1.09)*
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 (o), in dollars, of money in account B after r years.
r (number of years) 1 2
3
4
g() (amount in dollars) 1,375 1,512.50 1,663.75 1,830.13
Which account recorded a greater percentage change in amount of money over the previous year? Justify your answer. (5 points)

Increase in account A by a rate of 9%

Account B is increasing at a rate of 10% per year

ACCOUNT B recorded a greater percentage change in amount of money.

Step-by-step explanation:

Given that :

Amount in account A:

f(x) = 1,264(1.09)*

Writing out the general formula :

F(x) takes the form of an exponential function.

In the form:

F(x) = ab^x

b = base

b = 1.09 since b > 1 ; then b represents exponential growth

Hence,

F(x) can be expressed as :

y = a(1 + b)

b = growth or Decay factor

Here

1 + rate = 1.09

Rate = 1.09 - 1

Rate = 0.09

Rate = 0.09 * 100% = 9%

Increase in account A by a rate of 9%

ACCOUNT B:

Number of years (r) _ 1 ___ 2 3 4

Amountin$g(r) _ 1375 _1512.50_1663.75_1830.13

change in amount :

Taking the first and second year :

((1512.50 - 1375) / 1375) * 100%

(137.5 / 1375) * 100%

0.1 * 100% = 10%

Account B is increasing at a rate of 10% per year

Hence, ACCOUNT B recorded a greater percentage change in amount of money

Exponential

you can plot the points on a graphing calculator

Step-by-step explanation: