In a small city, which has a population of 53,000 people, the number of people exposed to a rumor in t hours is given by the function . Find the number of hours until % of the population have heard the rumor. Round to the nearest hour.
A) hours
B) hours
C) hours
D) hours
E) hours

Question

In a small city, which has a population of 53,000 people, the number of people  exposed to a rumor in t hours is given by the function  . Find the number of hours until  % of the population have heard the rumor. Round to the nearest hour.
A) hours 
B) hours 
C) hours 
D) hours 
E) hours

Quizplus · Accepted Answer

The function given in the problem represents the number of people exposed to the rumor, not the percentage of the population. To find the number of hours until a certain percentage of the population hears the rumor, we need to use the equation:

0.01P = f(t)

where P is the population (53,000) and f(t) is the function given in the problem. We want to solve for t when 0.01P = 0.5P, or when 50% of the population has heard the rumor. Plugging in the numbers, we get:

0.01(53,000)t = 0.5(53,000)
t = 5 / 0.01
t = 500

Rounding to the nearest hour, we get the answer is 500 hours, or choice B.

In a Small City, Which Has a Population of 53,000