Question

The amount of money, in dollars, in a savings account after x years is given by M(x) = 10,000(1.03)x. What does the value 1.03 represent?

A) The original deposit was $103.
B) There is a 3 percent increase in the savings account each year.
C) The savings account earns $103 interest per month.
Eliminate
D) There is a 103 percent increase in the savings account each year.

Answer 1

B)

There is a 3 percent increase in the savings account each year.

Explanation:

There is a 3 percent increase in the savings account each year.

M(x) = 10,000(1.03)x → 1.03 = 103% = 100% + 3% growth → This is a 3 percent increase each year.

Answer 2

Option B) There is a 3 percent increase in the savings account each year.

Explanation:

we have

`M(x)=10,000(1.03^x)`

This is a exponential function of the form

`y=a(b^x)`

where

M(x) represent the amount of money in a saving account

x represent the number of years

a is the original deposit (y-intercept)

b is the base

r is the rate or percent increase

`b=(1+r)`

The percent increase per year is the base of the exponential function decreased by 1.

so

`r=b-1`

In this problem we have

`a=\$10,000` ---> original deposit

`b=1.03\\r=1.03-1=0.03=3\%`

Therefore

The percent increase per year is 3%