Question

The resale value V, in thousands of dollars, of a boat is a function of the number of years t since the start of 2011, and the formula is

V = 12.5 − 1.3t.
(a) Calculate V(3).
(b) In what year will the resale value be 7.3 thousand dollars?
(c) Solve for t in the formula above to obtain a formula expressing t as a function of V.
(d) In what year will the resale value be 3.4 thousand dollars?

Answer 1

a) V(3) = 8.6.

b) The resale value will be 7.3 thousand dollars at the start of 2015.

c)
`t(V) = (12.5 - V)/(1.3)`

d) 2017

Explanation:

We are given the following function:

`V(t) = 12.5 - 1.3t`

(a) Calculate V(3).

This is V when t = 3. So

`V(3) = 12.5 - 1.3(3) = 8.6`

So

V(3) = 8.6.

(b) In what year will the resale value be 7.3 thousand dollars?

t years after the start of 2011, and t is found when
`V(t) = 7.3`. So

`V(t) = 12.5 - 1.3t`

`7.3 = 12.5 - 1.3t`

`1.3t = 5.2`

`t = (5.2)/(1.3)`

`t = 4`

2011 + 4 = 2015

The resale value will be 7.3 thousand dollars at the start of 2015.

(c) Solve for t in the formula above to obtain a formula expressing t as a function of V.

`V(t) = 12.5 - 1.3t`

`1.3t(V) = 12.5 - V`

`t(V) = (12.5 - V)/(1.3)`

(d) In what year will the resale value be 3.4 thousand dollars?

t years after 2011, and t is found t when
`V = 3.4`. So

`V(t) = 12.5 - 1.3t`

`3.9 = 12.5 - 1.3t`

`1.3t = 8.6`

`t = (8.6)/(1.3)`

`t = 6.62`

2011 + 6.62 = 2017

So the year is 2017.