Question

Bella plans to put $200 into a savings account. She can place her money into an account represented by p(x) = 3x + 200, or into another account represented by n(x) = 200(1.04)x. Which account has the highest value in 4 years? Which account has the highest in 15 years?

Answer 1

p(x) = 3x + 200
x=4 ⇒ p(4) = 3(4)+200=12+200=212
x=15 ⇒ p(15) = 3(15)+20=45+200=245

n(x) = 200(1.04)^xx
=4 ⇒ n(4) = 200 (1.04)^4 = 233.97
x=15⇒n(15)=200(1.04)^15 = 360.19

Then n(x) has the highest value in 4 years; n(x) has the highest value in 15 years

Answer 2

n(x) has the highest value in 4 years

and n(x) has the highest value in 15 years

Explanation:

p(x) = 3x + 200

Putting x=4

⇒ p(4) = 3×4+200

=12+200

=212

Putting x=15

⇒ p(15) = 3×15+200

=45+200

=245

n(x) =
`200* (1.04)^x`

Putting x=4

⇒ n(4) =
`200* (1.04)^4`

= 233.97

Putting x=15

⇒n(15)=
`200* (1.04)^(15)`

= 360.19

On comparing the values of n(x) and p(x) at x=4 and x=15,we get

n(x) has the highest value in 4 years

and n(x) has the highest value in 15 years