Exponential Decay Functions

Question 1

A farmer estimates that he has 9,000 bees producing honey on his farm. The farmer becomes concerned when he realizes the population of bees seems to be decreasing steadily at a rate of 5% per year. If the number of bees in the population after x years is represented by f(x), which statements about the situation are true? Check all that apply.The function f(x) = 9,000(1.05)x represents the situation. The function f(x) = 9,000(0.95)x represents the situation. After 2 years, the farmer can estimate

Revolt · Accepted Answer

The function f(x) = 9,000(0.95)x represents the situation.; After 2 years, the farmer can estimate that there will be about 8,120 bees remaining.; The range values, in the context of the situation, are limited to whole numbers.

Question 2

What did you include in your response? Check all that apply.

Revolt · Accepted Answer

The graphs are reflections of each other over the y-axis.; The g(x) function represents exponential decay.; The f(x) function represents exponential growth.

Question 3

a = [___]

Revolt · Accepted Answer

77442; 77443; 1500

Question 4

b = [___]

Revolt · Accepted Answer

0.97

Question 5

How do the graphs of the functions f(x) = ()x and g(x) = ()x compare?

Revolt · Accepted Answer

The graphs of f(x) = (3/2)^x and g(x) = (2/3)^x are reflections of each other over the y-axis. The function f(x) represents exponential growth because the base 3/2 is greater than 1, while g(x) represents exponential decay because the base 2/3 is between 0 and 1. Both functions have the same y-intercept at (0, 1).

Exponential Decay Functions Answers

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