A vehicle purchased for $\$ 29,800$ depreciates at a constant rate of $5 \%$. Determine the approximate value of the vehicle 13 years after purchase. Round to the nearest whole dollar.
Answer
Thus, the approximate value of the vehicle 13 years after purchase is \(\boxed{\$15,298}\).
Step 1 ：The problem provides that a vehicle was purchased for $29,800 and depreciates at a constant rate of 5% per year. We are asked to determine the approximate value of the vehicle 13 years after purchase.
Step 2 ：We can model the depreciation of the vehicle's value with the formula \(V = P * (1 - r)^t\), where \(V\) is the final value, \(P\) is the initial value, \(r\) is the rate of depreciation, and \(t\) is the time in years.
Step 3 ：Given that \(P = \$29,800\), \(r = 5% = 0.05\), and \(t = 13\) years, we can substitute these values into the formula.
Step 4 ：Doing so, we find that \(V = \$29,800 * (1 - 0.05)^{13}\).
Step 5 ：Calculating the above expression, we find that \(V = \$15,298\).
Step 6 ：Thus, the approximate value of the vehicle 13 years after purchase is \(\boxed{\$15,298}\).
