Question

The resale value V, in thousands of dollars, of a boat is a function of the number of years since the start of 2011, and the formula isV = 10.5 - 1.1t.(a) Calculate V(3).________thousand dollarsExplain in practical terms what your answer means.This means that the resale value of the boat will be______thousand dollars at the start of the year_______(b) In what year will the resale value be 6.1 thousand dollars?______(c) Solve for t in the formula above to obtain a formula expressing t as a function of V. t=______(d) In what year will the resale value be 2.8 thousand dollars?_______

Answer 1

a) V (3) = 7.2 thousand dollars.

In practical terms, the resale value of the boat will be 7.2 thousand dollars at the start of the year 2014.

b) t = 4years.

The resale value will be 6.1 thousand dollars in the year 2015.

c) t = 9.545 - 0.909V

d) t = 7 years.

7 years after the start of 2011 = 2018.

Step-by-step explanation

We are given that the resale value (V), in thousands of dollar, of a boat is given as

V = 10.5 - 1.1t

where t = number of years since the start of 2011.

a) We are told to calculate V(3).

V = 10.5 - 1.1t

t = 3

V = 10.5 - 1.1 (3)

V = 10.5 - 3.3

V = 7.2 thousand dollars.

In practical terms, the resale value of the boat will be 7.2 thousand dollars at the start of the year 2014.

b) In what year will the resale value be 6.1 thousand dollars.

V = 10.5 - 1.1t

what is t when V = 6.1

6.1 = 10.5 - 1.1t

1.1t = 10.5 - 6.1

1.1t = 4.4

Divide both sides by 1.1

(1.1t/1.1) = (4.4/1.1)

t = 4 years.

4 years afther the start of 2011 = 2015.

c) We are asked to solve for t and obtain a formula expressing t as a function of V.

V = 10.5 - 1.1t

1.1t = 10.5 - V

Divide through by 1.1

`\begin{gathered} (1.1t)/(1.1)=(10.5)/(1.1)-(V)/(1.1) \\ t=9.545-(V)/(1.1) \\ t=9.545-0.909V \end{gathered}`

t, expressed in terms of V, is t = 9.545 - 0.909V

d) We are now asked to calculate in what year will the resale value be 2.8 thousand dollars.

t = 9.545 - 0.909V

t = 9.545 - 0.909 (2.8)

t = 9.545 - 2.545

t = 7 years.

7 years after the start of 2011 = 2018.

Hope this Helps!!!