Profit from the sale of cars at a local car lot decreased rapidly between the years 2018 and 2022 according to the model \( P^{\prime}(t)=5306 e^{-0.04606 t} \) where \( t=0 \) represents the year 2018 . If this trend continues in the future, estimate the total profit from the sale of cars from 2018 onward. (Round your answer to the nearest dollar.)

To find the total profit from the sale of cars from 2018 onward, you need to evaluate the integral of the profit rate function \( P^{\prime}(t) \) from \( t = 0 \) to \( t = \infty \). The profit rate function is given by: \[ P^{\prime}(t) = 5306 e^{-0.04606 t} \] To find the total profit \( P \), we calculate: \[ P = \int_{0}^{\infty} P^{\prime}(t) \, dt = \int_{0}^{\infty} 5306 e^{-0.04606 t} \, dt \] The integral of \( e^{-kt} \) from 0 to infinity is \( \frac{1}{k} \). Here, \( k = 0.04606 \). Therefore, \[ P = 5306 \cdot \int_{0}^{\infty} e^{-0.04606 t} \, dt = 5306 \cdot \frac{1}{0.04606} \] Calculating the integral: \[ P = 5306 \cdot \frac{1}{0.04606} \approx 115,067.32 \] Rounding to the nearest dollar, the estimated total profit from the sale of cars from 2018 onward is approximately \( \boxed{115067} \) dollars.