Answer:
$8,327.61
Step-by-step explanation:
To calculate the value of Brianna's car after t years of depreciation, we can use the formula for exponential decay:
[tex]\boxed{\begin{array}{l}\underline{\textsf{Exponential Decay}}\\\\FV = A(1 - r)^t\\\\\textsf{where:}\\\\ \phantom{ww}\bullet\;\textsf{$FV$ is the future value.}\\ \phantom{ww}\bullet\;\textsf{$A$ is the initial amount.}\\\phantom{ww}\bullet\;\textsf{$r$ is the rate of decay (in decimal form).}\\\phantom{ww}\bullet\;\textsf{$t$ is the time (in years).}\\ \end{array}}[/tex]
Given that Brianna bought her first car for $53671, and it is expected to depreciate at an average of 17% each year during the first 10 years, then:
- A = $53,671
- r = 17% = 0.17
- t = 10 years
Substitute the values into the formula and solve for FV:
[tex]FV=53671(1-0.17)^{10}\\\\\\FV=53671(0.83)^{10}\\\\\\FV=53671(0.15516041...)\\\\\\FV=8327.614465...\\\\\\FV=\$8,327.61\; \sf (nearest\;cent)[/tex]
Therefore, the value of Brianna's car in 10 years will be:
[tex]\Large\boxed{\boxed{\$8,327.61}}[/tex]
