Question

A company is hoping to expand its facilities but needs capital to do so. In an effort to position itself for expansion in 3 years, the company will direct half of its profits into investments in a continuous manner. The company's profits for the past 5 years are shown in the table. The company's current yearly profit is $1,160,000. (The current year corresponds to t = 0.)

Profit over the Past Five Years

Years Ago	5	4	3	2	1
Profit (thousand dollars)	860	900	930	1000	1060

Consider the following profit scenarios and answer the questions.

(a) The profit for the next 3 years follows the trend shown in the table.
(i) Write the quadratic function that describes the flow of the company's investments. (Align the input such that 5 years ago corresponds to t = −5. Round all numerical values to three decimal places.)
R(t) = ______thousand dollars

(ii) Calculate the capital the company will have saved after 3 years of investing at 6.4% annual interest compounded continuously. (Round your answer to three decimal places.)
$ _____thousand
(b) The profit increases each year for the next 3 years by the same percentage that it increased in the current year.(i) Write the function that describes the flow of the company's investments. (Round all numerical values to three decimal places.)
R(t) = ______ thousand dollars

(ii) Calculate the capital the company will have saved after 3 years of investing at 6.4% annual interest compounded continuously. (Round your answer to three decimal places.)
$ ______ thousand
(c) The profit remains constant at the current year's level.(i) Write the function that describes the flow of the company's investments.
R(t) = ______thousand dollars

(ii) Calculate the capital the company will have saved after 3 years of investing at 6.4% annual interest compounded continuously. (Round your answer to three decimal places.)
$ _____ thousand
(d) The profit increases each year for the next 3 years by the same fixed amount that it increased this year.(i) Write the function that describes the flow of the company's investments.
R(t) = ______thousand dollars

(ii) Calculate the capital the company will have saved after 3 years of investing at 6.4% annual interest compounded continuously. (Round your answer to three decimal places.)
$_______   thousand

Answer 1