The number of printers sold since 2003 at Mike's office supply store can be modeled by the function N (t) = 15t + 85 and the price per printer can be modeled by P (t) = 15t2-32t+126, where t is the number of years since 2003. According to this model, what is the total amount of revenue generated by the sales of printers in the office supply store in 2009? Round your answer to the nearest cent.

The total amount of revenue is $82950

Step-by-step explanation:

* Lets explain how to solve the problem

- The number of printers sold since 2003 at Mike's office supply store

can be modeled by the function N (t) = 15t + 85

∴ The number of printers is N (t) = 15t + 85

- The price per printer can be modeled by P (t) = 15t² - 32t + 126

∴ The price per printer is P (t) = 15t² - 32t + 126

- t is the number of years since 2003

- The amount of revenue is the product of the number of printers

sold and the price per printer

∴ Revenue = N (t) * P (t)

- We need to find the total amount of revenue generated by the

sales of printers in the office supply store in 2009

∵ t is the number of years since 2003

∴ In 2009 t = 2009 - 2003 = 6 years

∵ t = 6 years

∵ N (t) = 15t + 85

∴ N (6) = 15 (6) + 85 = 175

∴ They sold 175 printers from 2003 to 2009

∵ t = 6 years

∵ P (t) = 15t² - 32t + 126

∴ P (6) = 15 (6) ² - 32 (6) + 126 = 474

∴ The price per printer is $474

∵ Revenue = N (t) * P (t)

∴ Revenue = 175 * 474 = 82950

* The total amount of revenue is $82950