Jeff bought a new car for $10,450. He knows this car's value will decrease by 20% each year. Jeff writes the following function to model the cost of his car after \( t \) years:

\[ C(t) = 10,450(0.80)^t \]

If Jeff plans to sell the car after five years, what will be the value of the car at that time, to the nearest dollar?

The value of the car after five years will be: $3424.26
What is the future value of the car?
We are told that Jeff bought a new car $10,450
function to model the cost of his car after t years is:
C(t) = 10450 ( 0.80 ) t
Thus:
To find the value of the car after five years, we can plug in t = 5 into the function
C(t) = 10450 ( 0.80 ) t
C(5)&=10,450(.80)^5
C(5) = $3424.26
So, the value of the car after five years will be approximately $3424.26

Answered by AFOKE88 | 2024-06-25

The value of the car after 5 years would be approximately $3423.44.
To find the value of the car after t years using the function C ( t ) = 10 , 450 ( 0.80 ) t , we substitute the value of t into the function.
Given that Jeff plans to sell the car after t years, we need to evaluate C(t) for the given value of t .
Let's calculate:
C(t) &= 10,450 \times (0.80)^t \\\\C(5) &= 10,450 \times (0.80)^5 \\\\&= 10,450 \times 0.32768 \\\\&\approx 3423.44
So, the value of the car after 5 years would be approximately $3423.44.

Answered by PragatiR | 2024-06-25

After five years, Jeff's car will be worth approximately $3,429. We used the function C ( t ) = 10 , 450 ( 0.80 ) t to calculate this value. By plugging in t = 5 , we found the depreciation to be significant over that period.
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Answered by AFOKE88 | 2024-12-17