Dr. Who owns a phone booth worth $7,500, which, for tax purposes, is assumed to depreciate linearly to zero over a 15 year period. a. Express the value of the doctor's phone booth as a function of time. b. What is the value of the phone booth after 6 years?

a. y = 7500 - 500x

b. $ 4,500

Step-by-step explanation:

a. Given,

The original value of the phone = $ 75,00

Let the linear function that shows the value of booth after x years,

y = b - ax,

For x = 0 years, y = 7500

⇒ 7500 = b - a (0) ⇒ b = 7500

For x = 15, y = 0,

0 = b - 15x ⇒ 0 = 7500 - 15a ⇒ 15a = 7500 ⇒ a = 500

Hence, the function that shows the value of car after x years,

y = 7500 - 500x

b. if x = 6,

The value of the booth after 6 years would be,

y = 7500 - 500 (6) = 7500 - 3000 = $ 4,500