Question

Cheyanne plans to put $150 into a savings account. she can place her money into an account represented by f(x)=5x+150, or into another account represented by g(x)=150(1.03)^x. which account has the highest value in 3 years? which account has the highest value in 10 years?

1. f(x) has the highest value in 3 years; g(x) has the highest value in 10 years

2. g(x) has the highest value in 3 years; f(x) has the highest value in 10 years

3. f(x) has the highest value in 3 years; f(x) has the highest value in 10 years

4.g(x) has the highest value in 3 years; g(x) has the highest value in 10 years

Answer 1

Answer: 1. f(x) has the highest value in 3 years; g(x) has the highest value in 10 years

Explanation:

Given:- Principal amount= $150

First account represented by the function=
`f(x)=5x+150`→Linear function

Second account represented by the function=
`g(x)=150(1.03)^x`→Exponential function

where x is the time period in years.

When x=3 years

`f(3)=5(3)+150=15+150=\$165`

`g(3)=150(1.03)^3=\$163.90`

here, f(x) has the highest value .

When x=10 years

`f(10)=5(10)+150=50+150=\$200`

`g(10)=150(1.03)^(10)=\$201.58`

g(x) has the highest value.

Therefore, f(x) has the highest value in 3 years; g(x) has the highest value in 10 years