Question

Edward plans to put $75 into a savings account. He can place his money into an account represented by b(x) = 7x + 75, or into another account represented by c(x) = 75(1.06)x. Which account has the highest value in 2 years? Which account has the highest in 12 years?

A.) c(x) has the highest value in 2 years; c(x) has the highest value in 12 years

B.) b(x) has the highest value in 2 years; b(x) has the highest value in 12 years

C.) c(x) has the highest value in 2 years; b(x) has the highest value in 12 years

D.) b(x) has the highest value in 2 years; c(x) has the highest value in 12 years

Answer 1

Answer: B

Step-by-step explanation: b(x) is highest all the time

Answer 2

Let

x------> the time in years

b(x)----> the value in dollars of a saving account

c(x)----> the value in dollars of another account

we know that

`b(x)=7x+75`

`c(x)=75(1.06)^(x)`

Step 1

Find the value of each account for
`x=2\ years`

`b(2)=7*2+75=\$89`

`c(2)=75(1.06)^(2)=\$84.27`

so

`b(2) > c(2)`----> b(x) has the highest value in
`2` years

Step 2

Find the value of each account for
`x=12\ years`

`b(12)=7*12+75=\$159`

`c(12)=75(1.06)^(12)=\$150.91`

so

`b(12) > c(12)`----> b(x) has the highest value in
`12` years

therefore

the answer is the option B

b(x) has the highest value in
`2` years; b(x) has the highest value in
`12` years