Question

The equation N(t) = 450 models the number of people in a town who have heard a rumor 1 + 49e^(0.7t) after t days. As t increases without bound, what value does N(t) approach? Interpret your answer: How many people started the rumor? Number N(t) approaches Number.

Answer 1

The value N(t) approaches 450. The maximum number of people who have heard the rumor is 450.

Step-by-step explanation:

The equation N(t) = 450 models the number of people in a town who have heard a rumor 1 + 49e^(0.7t) after t days. As t increases without bounds, the value N(t) approaches 450. This means that the number of people who have heard the rumor reaches a maximum of 450 as time goes on.

Interpretation: The value N(t) = 450 represents the maximum number of people who have heard the rumor. It suggests that there is a limit to how many people can hear the rumor, and once that limit is reached, the number of people who hear the rumor does not increase any further.

Answer 2

The equation N(t) = 450 models the number of people in a town who have heard a rumor after t days. As t increases without bound, N(t) approaches infinity. There is no limit to the number of people who have heard the rumor in the town.

Step-by-step explanation:

The equation N(t) = 450 models the number of people in a town who have heard a rumor 1 + 49e^(0.7t) after t days. As t increases without bound, N(t) approaches a specific value. This value can be found by taking the limit as t approaches infinity. In this case, the limit is found by evaluating the expression 49e^(0.7t) as t approaches infinity. Since the base of the exponential function (e) is a positive number greater than 1, the exponential function will approach infinity as t approaches infinity. Therefore, N(t) approaches infinity as t increases without bound.

Interpretation: As time goes on, the number of people who have heard the rumor will continue to increase without limit. This means that there will be no limit to the number of people who have heard the rumor in the town. It is not possible to determine the number of people who started the rumor based on the given equation.