Question

The annual passenger revenue of a rail transport corporation from the year 2000 to the year 2020 is modeled by the formula R=−20|t−15|+1,010 where R is the annual revenue in million dollars and t is the number of years since 2000. Select all the years where the passenger revenue was $930 million.

A.2011
B.2012
C.2018
D.2019
E.2020

Answer 1

The years where the passenger revenue was $930 million are not within the given time frame.

Step-by-step explanation:

To find the years where the passenger revenue was $930 million, we need to solve the equation R = 930. Substituting the given equation R = -20|t-15| + 1010, we have -20|t-15| + 1010 = 930.

Solving for |t-15|, we get |t-15| = 40. Since the absolute value of a quantity is always positive, we have two possible cases.

Case 1: t - 15 = 40. Solving for t, we get t = 55.

Case 2: -(t - 15) = 40. Solving for t, we get t = -25. Since negative years do not make sense in this context, we can ignore Case 2.

Therefore, the year where the passenger revenue was $930 million is t = 55, which corresponds to the year 2055.

However, the provided interval is from the year 2000 to the year 2020. Therefore, none of the options A, B, C, D, or E correspond to the year where the passenger revenue was $930 million.