Answer:
13, i think.
Step-by-step explanation:
use the equation: p( 1 - 7.5/100)^r
p= original amount
r = years
sub in numbers
22300 ( 1- 7.5/100)^r
just sub in different numbers for r till you get closest to your answer
After 13 years the value of the car would be $7700
"It describes the decrease in an amount by a consistent percentage rate over a period of time."
"f(t) = a(1 - r)^t , where t is time, a is the initial value and r is the rate"
For given example,
initial value of the car (a) = 22300
The value of the car depreciates at 7.5% per year.
So, the rate (r) = 7.5%
We can write 7.5 percent as,
7.5% = 7.5/100
= 0.075
So, r = 0.075
Let 't' represents the number of years
We need to find the number of years when the car value is 7700 dollars.
y = $7700
Using the formula of exponential decay,
⇒ y(t) = a × (1 - r)^t
⇒ 7700 = 22300 × (1 - 0.075)^t
⇒ 0.3453 = (0.925)^t
⇒ t = 13.63
⇒ t ≈ 13
Therefore, after 13 years the value of the car would be $7700
Learn more about an exponential decay here:
https://brainly.com/question/14355665
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