Adelivery truck is purchased new for $54,000.
a. write a linear function of the form y = mt + b to represent the value y of the vehicle t years after purchase. assume that the vehicle is depreciated by $ 6750 per year.
b. suppose that the vehicle is depreciated so that it holds 70% of its value form the previous year. write an exponential function of the form y = vobt where v0 is the initial value and t is the number of years after purchase.
c. to the nearest dollar, determine the value of the vehicle after 4 yr and after 8 yr using the linear model.
d. to the nearest dollar, determine the value of the vehicle after 4 yr and after 8 yr using the exponential model.

Part a)

Part b)

Part c) The value of the vehicle after 4 yr is $27,000 and the value of the vehicle after 8 yr is $0

Part d) The value of the vehicle after 4 yr is $12,965 and the value of the vehicle after 8 yr is $3,113

Step-by-step explanation:

Part a) Write a linear function

Let

y -----> the value of the vehicle

t ----> the time in years after purchase

The equation in slope intercept form is equal to

where

m is the slope

b is the y-intercept (original value)

we have

substitute

Part b) write an exponential function of the form

we have

substitute

Part c) To the nearest dollar, determine the value of the vehicle after 4 yr and after 8 yr using the linear model

For t=4 year

substitute

For t=8 year

substitute

Part d) To the nearest dollar, determine the value of the vehicle after 4 yr and after 8 yr using the exponential model.

For t=4 year

substitute

For t=8 year

substitute

If they met half-way, each train traveled 360 milet s = speed of the slower trainthen(s+4) = speed of the faster train: write a time equationslow train time - fast train time = 1 hr  -   = 1multiply equation by s(s+4), cancel the denominators
360(s+4) - 360s = s(s+4)360s + 1440 - 360s = s^2 + 4sa quadratic equation0 = s^2 + 4s - 1440use the quadratic formula; a=1; b=4; c=-1440. but this will factor to: (s-36)(s+40) = 0positive solutions = 36 mph, speed of the slow trainthen obviously; 40 mph, the speed of the faster  source: