Respuesta :
Answer: Initial value of car = $ 27500
And, the value of car after 13 years is $5219.242
Step-by-step explanation:
Here, the given function that models the price of car after t years,
[tex]v(t) = 27500(0.88)^t[/tex]
Since, initially, t = 0
Thus, the initial value of the car,
[tex]v(0) = 27500(0.88)^0=27500[/tex]
Now, after 13 years, t = 13
Thus, the value of car after 13 years,
[tex]v(13)=27500(0.88)^{13}[/tex]
= [tex]27500\times 0.189790617123[/tex]
= [tex]5219.24197088\approx 5219.242[/tex]
Answer:
Current value is $27500 and the value after 13 years will be $20417.
Step-by-step explanation:
The dollar value v(t) of a certain car model in t years is given by the exponential function [tex]v(t)=27500\times(0.88)^{t}[/tex]
Now we have to find the initial value and the value after 13 years.
Therefore to calculate the initial value of the car v(0)=27500\times(.88)^{0}
= 27500×1 (since [tex]x^{0}=1[/tex]
So the current value of the car is $27500.
Now we will calculate the value of car after 13 years.
v(13) = [tex]27500(0.88)^{13}[/tex]
Now we take the log on both the sides of the equation
[tex]logv(13)=log\left \{ 27500\times (.88)^{13} \right \}[/tex]
[tex]=log 27500+13log(.88)[/tex]
= 4.44 + 13log(88÷100)
= 4.44 + 13( log88 - log100)
= 4.44+ 13(1.94-2)
log v(13)= 4.44 - 13(.056)
= 4.44- 0.72
= 3.72
⇒ v(13) = [tex]10^{3.72}[/tex] = 20417.38 ≈ $20417
