IM Alg1.5.5 Practice: Representing Exponential Decay

A population

of migrating butterflies satisfies the equation

where

is the number of weeks since they began their migration. Complete the table with the population after different numbers of weeks.

Graph the butterfly population. Think carefully about how to choose a scale for the axes.

What is the vertical intercept of the graph? What does it tell you about the butterfly population?

About when does the butterfly population reach 50,000?

Find the coordinates of the points labeled , , and . Explain your reasoning.

Select all statements that are true.

Select all that apply

A
The amount of the chemical in the water sample is decreasing exponentially.
B
The amount of the chemical in the water sample is not decreasing exponentially.
C
It is not possible to tell for certain whether or not the amount of the chemical is decreasing exponentially.
D
When it was first measured, there were 2,000 mg of the chemical in the water sample.
E
After 4 hours, there were 100 mg of the chemical in the water.

Could the amount of this chemical in the patient be decaying exponentially? Explain how you know.

The height of a plant in mm is 7. It doubles each week. Select all expressions that represent the height of the plant, in mm, after 4 weeks.

Select all that apply

What do you notice about the difference in the number of people who have read the book from month to month?

What do you notice about the factor by which the number of people changes each month?

If people have read the book one month, how many people will have read the book the following month?