Answer:
$52,590.16
Step-by-step explanation:
To calculate the value of Sam's truck after 3 years with an initial value of $71,021 and an annual depreciation rate of 9.5%, you can use the formula for exponential decay:
[tex]\sf V = P \times (1 - r)^n[/tex]
where:
- V is the final value after (n) years,
- P is the initial value,
- r is the annual depreciation rate (as a decimal),
- n is the number of years.
Given:
Plugging these values into the formula:
[tex]\sf V = 71,021 \times (1 - 0.095)^3[/tex]
First, calculate 1 - 0.095:
[tex]\sf 1 - 0.095 = 0.905[/tex]
Next, raise 0.905 to the power of 3:
[tex]\sf 0.905^3 \approx 0.7406[/tex]
Finally, multiply by the initial value:
[tex]\sf V = 71,021 \times 0.7406 \approx 52,590.16[/tex]
So, the value of Sam's truck after 3 years will be approximately $52,590.16.
Note: You can solve it in another way by decreasing each continuous value by 9.5% Three times.
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