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

Answer:

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

Step-by-step 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%

Answer 2

Answer:

B)  

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

Step-by-step 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.