A car was valued at \( \$ 43,000 \) in the year 2009 . By 2013 , the car value had depreciated to \( \$ 17,000 \). If the car's value continues to drop by the same percentage, what will it be worth in 2018 ? Round to the nearest dollar.

To determine the car's value in 2018, we'll follow these steps: 1. **Determine the Annual Depreciation Rate:** - **Initial Value (2009):** \$43,000 - **Value in 2013:** \$17,000 - **Time Period:** 4 years The depreciation can be modeled using the formula: \[ V = V_0 \times (1 - r)^t \] Where: - \( V \) = final value - \( V_0 \) = initial value - \( r \) = annual depreciation rate - \( t \) = time in years Plugging in the known values: \[ 17,000 = 43,000 \times (1 - r)^4 \] \[ (1 - r)^4 = \frac{17,000}{43,000} \approx 0.39535 \] Taking the fourth root: \[ 1 - r \approx \sqrt[4]{0.39535} \approx 0.7929 \] \[ r \approx 1 - 0.7929 = 0.2071 \text{ or } 20.71\% \] 2. **Calculate the Value in 2018:** - **Time from 2013 to 2018:** 5 years - **Value in 2013:** \$17,000 Using the depreciation formula again: \[ V_{2018} = 17,000 \times (1 - 0.2071)^5 \] \[ V_{2018} \approx 17,000 \times (0.7929)^5 \approx 17,000 \times 0.312814 \approx 5,317.84 \] Rounding to the nearest dollar: \[ V_{2018} \approx \$5,318 \] **Answer:** In 2018, the car will be worth approximately **\$5,318**.