Question

r(t)=0.5t 2 −2t+5 million dollars gives the cumulative revenue for Widgit Company, LLC, where t is the number of years since the start of the business at the end of 2000,3≤t≤18. Checkpoint: r(2)=3 a. When, after the start of the business, did cumulative revenue first hit 70 million dollars? Find the answer correct to three decimal places. In what month and year did the cumulative revenue first hit 70 million dollars? b. According to the model, what is the predicted cumulative revenue for Widgit Company, LI. at the end of 2020 ? Round to three decimal places and include units with the answer. c. Write the following statement in function notation. At the end of 2004 the cumulative revenue earned by WidgitCo was 5 million dollars.

Answer 1

a. To find when the cumulative revenue first hit 70 million dollars, we need to solve the equation 0.5t² - 2t + 5 = 70. This is equivalent to solving the quadratic equation 0.5t² - 2t - 65 = 0 for t. This yields two solutions, but since t represents time in years and is used here as a measure of time elapsed since the start of the business, we only keep the positive solution. We'll also convert the decimal part to months by multiplying it by 12.

b. The model predicts that the cumulative revenue for Widgit Company, LLC, at the end of 2020 can be obtained by substituting t = 20 into the equation for r(t), so r(20) = 0.5(20)² - 2(20) + 5.

c. At the end of 2004, the cumulative revenue earned by WidgitCo was 5 million dollars. In function notation, this statement can be written as r(4) = 5, where r is the function that gives the cumulative revenue for any given year t since the start of the business.