Question

The function V(t):= - 3500t+20000, where V is value and t is time in years, can be used to find the value of a large copy machine during the first 5 years of use.a. What is the value of the copier after 2 years and 6 months?After 2 years and 6 months, the copier is worth $b. What is the salvage value of the copier if it is replaced after 5 years?After 5 years, the salvage value of the copier is S.c. State the domain of this function.d. Sketch the graph of this function.e. What is the range of the function? _ < V(t) < _ f. After how many years will the copier be worth only $10,000? Round to 2 decimal places. After _ years, the copier will be worth only $10,000.

Answer 1

Given:

A function is given as V(t) = -3500t+20000, where V is value and t is time in years.

Find:

we have to answer the questions from (a) to (f).

Step-by-step explanation:

(a) The value of the copier after 2 years and 6 months (i.e. at t = 2.5) is

V(2.5)= - 3500(2.5)+20000 = -8750+20000 = $11250.

(b)The Salvage value of copier after 5 year (i.e. at t = 5) is

V(5) = -3500(5) + 20000 = -17500+20000 = $2500

(c)The domain of the function V(t) = -3500t + 20000 is [0,5.7143) as the value of machine cannot be negative.

(d) The graph of the function is given as below

(e)The range of the function V(t) is [0,20000].

(f)The time after the copier will be worth $10000 is

10000 = -3500t + 20000

3500t = 20000 - 10000

3500t = 10000

t = 10000/3500

t = 2.86years