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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.

Respuesta :

calculista

Answer:

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

Step-by-step explanation:

we have

[tex]M(x)=10,000(1.03^x)[/tex]

This is a exponential function of the form

[tex]y=a(b^x)[/tex]

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

[tex]b=(1+r)[/tex]

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

so

[tex]r=b-1[/tex]

In this problem we have

[tex]a=\$10,000[/tex] ---> original deposit

[tex]b=1.03\\r=1.03-1=0.03=3\%[/tex]

Therefore

The percent increase per year is 3%

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.

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