Respuesta :
Answer:
Option A is correct
[tex]f(x) = 20,000 \cdot (0.85)^x[/tex]
Step-by-step explanation:
An exponential function is given by:
[tex]f(x) = a(1+r)^x[/tex]
where,
f(x) represents the value after x years,
a is the initial value and
r is the rate(in decimal)
As per the statement:
Terrence buys a new car for $20,000.
⇒ a = $ 20,000
It is also given that:
The value of the car depreciates by 15% each year.
⇒r = -0.15
Then, substitute these value we get;
[tex]f(x) = 20,000 \cdot (1-0.15)^x[/tex]
⇒[tex]f(x) = 20,000 \cdot (0.85)^x[/tex]
Therefore, the function that represents the car's value is, [tex]f(x) = 20,000 \cdot (0.85)^x[/tex]
To solve the problem we must know about depreciation.
What is depreciation?
Depreciation is the rate by which the value of an object reduces with respect to time. it is given by the formula,
[tex]A= P(1-r)^t[/tex]
where A is the value of object after x period of time, P is the principal amount, r is the rate of depreciation, and t is the for the time period.
The value of Terrence's car after x years is [tex]A= 20,000(1-0.15)^x[/tex].
Given to us
- Terrence buys a new car for $20,000,
- rate of depreciation = 15%,
Value of Terrence's car
We know the formula of the rate of depreciation,
[tex]A= P(1-r)^t[/tex]
substituting the values,
[tex]A= 20,000(1-0.15)^x[/tex]
Hence, the value of Terrence's car after x years is [tex]A= 20,000(1-0.15)^x[/tex].
Learn more about Depreciation:
https://brainly.com/question/3023490
