Certainly! The text from the image is as follows:---**2.** A small oil company considers the continuous pumping of oil from a well as a continuous income stream,\[ f(t) = 600e^{-0.2t} \]in thousands of dollars per year.Suppose that the oil company is planning to sell the well. The company establishes its selling price using the 'present value' of this well over the next 10 years.**b.** If the income can be invested at 10% compounded continuously, what is the estimated selling price of this well?---**Explanation:**The equation $ f(t) = 600e^{-0.2t} $ represents the continuous income stream from pumping oil, measured in thousands of dollars per year. Here, $ t $ is time in years, and the function models the income as it decreases exponentially over time.The problem involves calculating the present value of the income stream over a 10-year period if the income were invested at a continuous compound interest rate of 10%. This requires integrating the income function over the 10-year period and applying the formula for present value with continuous compounding. **Preceding Question:**A small oil company considers the continuous pumping of oil from a well as a continuous income stream, given by the function:\[ f(t) = 600e^{-0.2t} \]where $ f(t) $ is the income in thousands of dollars per year.**(a)** Find an estimate of the total income from this well over the next 10 years.**Expert Solution****Step 2**To find the estimated total income over the next 10 years, we calculate:\[ f(10) = 600 \times e^{-0.2 \times 10} \]\[ = 600 \times e^{-2} \]\[ = 600 \times \frac{1}{e^2} \]\[ = \frac{600}{(2.7183)^2} \]\[ \approx 81.2000 \]So, the total income over the next 10 years is $\boxed{81.20}$ thousand dollars.

Note: The answer given in the preceding question is incorrect. We will solve first part (a) then part (b). Throughout the solution we will approximate the decimal values correct to two decimal places. Given: Income of the oil company ft=600e-0.2t in thousand dollars per year. To find: Estimate of the total income from the well over the next 10 years. Estimated selling price of the well if the income can be invested at 10% compounded continuously.(a) Given that the income is ft=600e-0.2t in thousand dollars per year. The total income over the next 10 years is given by the integral over 0 to 10 of f. Then, Total income=∫010ftdt=∫010600e-0.2tdt=600e-0.2t-0.2010=600-0.2e-0.210-e0=-3000e-2-1=30001-e-2=2593.99 Hence, the total income from the well over the next 10 years will be 2593.99 thousand dollars.(b) To find the estimated selling price of the well, we need to find the present value of the well using the total income obtained in part a. From part a, we got that the total income over 10 years is 2593.99 thousand dollars. Present value can be found using the formula below. Present value=Future value1+rn Substituting the future value FV=2593.99, rate of interest r=10%, and n=10, we get Present value=Future value1+rn=2593.991+0.110=2593.991.110=1000.0954≈1000.1 Hence, the estimated selling price of the well is 1000.1 thousand dollars.