Respuesta :

MoeezKhan

Answer:

The value of the car one year after purchase is approximately $25,480.

Step-by-step explanation:

To find the value of the car one year after purchase, we can use the formula for exponential decay:

Value after n years=Initial value×(1−Rate of depreciation)ⁿ

Given:

Initial value (V₀) = $28,000

Rate of depreciation (r) = 9% = 0.09 (as a decimal)

Time (t) = 1 year

Substituting the values into the formula:

V=28000×(1−0.09)¹

V=28000×(0.91)

V≈25480
To calculate the value of the car one year after purchase with a depreciation rate of 9% per year, you can use the following formula for exponential decay:

\[ V = V_0 \times (1 - r)^t \]

Where:
- \( V \) is the final value of the car after \( t \) years.
- \( V_0 \) is the initial value of the car (in this case, $28,000).
- \( r \) is the rate of depreciation per year (in decimal form, so 9% would be \( 0.09 \)).
- \( t \) is the time in years.

Given:
- \( V_0 = $28,000 \)
- \( r = 0.09 \) (9% in decimal form)
- \( t = 1 \) year

Substitute the values into the formula:

\[ V = 28000 \times (1 - 0.09)^1 \]

\[ V = 28000 \times (1 - 0.09) \]

\[ V = 28000 \times (0.91) \]

\[ V = 25480 \]

So, the value of the car one year after purchase is $25,480.

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