A company has introduced two new products to the market. The revenue generated by product A was $63,000 in the first year, and t
he revenue increases by 3.5% every year. The revenue generated by product B was $81,000 in the first year, and the revenue increases by 2.1% every year.
Which function can the company use to determine its total revenue from the two products, R(x), after they have been on the market for x years, and approximately what will be the revenue generated by sales of the products after 6 years?
For this case we have functions of the form: y = A (b) ^ x Where, A: initial amount b: growth rate x: time Therefore, substituting values we have: Product A: y = 63000 (1,035) ^ x Product B: y = 81000 (1,021) ^ x The sum of the products is: R (x) = 63000 (1,035) ^ x + 81000 (1,021) ^ x Rewriting: R (x) = 9000 (7 (1,035) ^ x + 9 (1,021) ^ x) Evaluating for 6 years: R (6) = 9000 * (7 * (1,035) ^ 6 + 9 * (1,021) ^ 6) R (6) = 169200 $ Answer: The revenue generated by sales of the products after 6 years is: R (x) = 9,000 [7 (1,035) x + 9 (1,021) x]; $ 169,200