Exponential Decay Functions

Question 1

Which function represents exponential decay?

Revolt · Accepted Answer

f(x) = 2()x

Question 2

Which graph represents exponential decay?

Revolt · Accepted Answer

[Image: On a coordinate plane, a curve approaches y = 0 in...]

Question 3

⇒ 18

Revolt · Accepted Answer

3

Question 4

Which statements describe the function f(x) = 3()x? Check all that apply.Each successive output is the previous output divided by 3.As the domain values increase, the range values decrease. The graph of the function is linear, decreasing from left to right.Each successive output is the previous output multiplied by 3.The range of the function is all real numbers greater than 0. The domain of the function is all real numbers greater than 0.

Revolt · Accepted Answer

Each successive output is the previous output divided by 3.; As the domain values increase, the range values decrease.; The range of the function is all real numbers greater than 0.

Question 5

Which function represents the given graph?

Revolt · Accepted Answer

f(x) = 100 · ()x

Question 6

A doctor estimates that a particular patient is losing bone density at a rate of 3% annually. The patient currently has a bone density of 1,500 kg/mg3. The doctor writes an exponential function to represent the situation. Which values should the doctor use for a and b in a function written in the form f(x) = abx, where f(x) represents the bone density after x years? a = b =

Revolt · Accepted Answer

Part 1: 1,500; Part 2: 0.97

Question 7

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 that there will be about 8,120 bees remaining. After 4 years, the farmer can estimate that there will be about 1,800 bees remaining. The domain values, in the context of the situation, are limited to whole numbers. The range values, in the context of the situation, are limited to whole numbers.

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 8

How do the graphs of the functions f(x) = ( [image 1] )x and g(x) = ( [image 2] )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 yaxis. 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 yintercept at (0, 1).

Question 9

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.; They have the same initial value.

Exponential Decay Functions Answers

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