Question

A town determined that the function f(x) - 820(0.977✕ models the number of speeding tickets issued in the town x years after 2000. Which statement is

true about the number of speeding tickets issued each year?
A) The number of speeding tickets decreases each year.

B) The number of speeding tickets remains constant each year.

C) The number of speeding tickets increases each year.

D) The number of speeding tickets fluctuates randomly each year.

Answer 1

The number of speeding tickets issued each year decreases because the function includes an exponential decay factor of 0.977, which is less than 1, indicating a decreasing quantity over time.

Step-by-step explanation:

Given the function f(x) = 820(0.977)^x, which models the number of speeding tickets issued in a town x years after 2000, we can determine whether the number of speeding tickets issued each year increases, decreases, remains constant, or fluctuates randomly.

The function includes an exponential decay factor of 0.977. Since this factor is less than 1, it indicates that the quantity is decreasing over time. Therefore, each subsequent year x, the factor 0.977^x becomes smaller, which means that the number of speeding tickets issued decreases as x increases.

Therefore, the correct statement about the number of speeding tickets issued each year is: A) The number of speeding tickets decreases each year.