Question

A company has introduced two new products to the market. The revenue generated by product A was $63,000 in the first year, and the 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?

R(x) = 9,000[7(1.035)x + 9(1.021)x]; $635,580
R(x) = 9,000[7(1.035)x + 9(1.021)x]; $169,200
R(x) = 9,000[9(1.035)x + 7(1.021)x]; $170,936
R(x) = 9,000[9(1.035)x + 7(1.021)x]; $688,050

Answer 1

The correct answer is R(x) = 9,000[9(1.035)x + 7(1.021)x]; $170,936

Answer 2

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