10. 0.72/1 points | Previous Answers LarCakc10 5.5.088 My Notes Ask Your Teacher

Question

10. 0.72/1 points | Previous Answers LarCakc10 5.5.088 My Notes Ask Your Teacher After t years, the value of a car purchased for $23,100 is given below nt) . 23,100 ( (a) Use a graphing utility to graph the function and determine the value of the car 4 years after it was purchased. (Round your answer to two decimal places) V(4) = $ 1 and t = 7 . (Round your answers to two decimal places.) (b) Find the rates of change of V with respect to t when t At t=1 Att=7 Enter a number (c) Use a graphing utility to graph Vt) and determine the horizontal asymptote of Vt) Horizontal asymptote: V' 0 As the car ages, it is worth less ' each year and depreciates less , each year, but the value of the car wil never , reach $0. Need Help? Read It Talk to a Tutor Submit Answer Save Progress Pracice Another Version

Explanation / Answer

V(t) = 23100 (6/7)^t

V(4) = $ 12468.81 ( from graphing utility )

b)

differentiating both sides with respect to t

dV/ dt = 23100 ln (6/7)(6/7)^t

dV / dt = -3560.88 (6/7)^t

at t = 1

-3052.18

at t = 7

= -1210.40

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