Modeling With Exponential Functions

In a carefully controlled biology lab, a population of 100 bacteria reproduces exponentially. Every hour, each bacteria splits into two bacteria.

Assuming no bacteria deaths, a function in the form

f(t) = ab^t can be used to model the growth of the bacteria population.

What would be the value of a?

• 100

• 0.5

• 2

• 50

In a carefully controlled biology lab, a population of 100 bacteria reproduces exponentially. Every hour, each bacteria splits into two bacteria.

Assuming no bacteria deaths, a function in the form

f(t) = ab^t can be used to model the growth of the bacteria population.

What would be the value of b?

• 100

• 0.5

• 50

• 2

The estimated population of elephants in northwestern Namibia and Etosha National Park are shown in the chart.

The elephant population in northwestern Namibia and Etosha National Park, f(b), can be predicted by the function , f(b) = 2,649(1.045)^b where b is the number of years since 1995.

What does the value 2,649 represent in this context?

• The predicted increase in the number of elephants in the region each year

• The predicted number of elephants in the region in 1995

• The year when the elephant population is predicted to stop increasing

• The percentage the elephant population is predicted to increase each year

Which of the following function describe exponential growth? Select all that apply.

• f(t) = 1.25^t

• f(t) = 2(0.93)^t

• f(t) = 3(1.07)^3t

• f(t) = 0.5(1.05)^t

• f(t) = 3(1.71)^5t

The value of Amy's car depreciated each year after she bought it.

The function v(t) = 24,893(0.88)^t represents the value of Amy's car t years after she bought it.

What is the rate of depreciation?

• 0.12%

• 0.88%

• 12%

• 88%

Considering the function f(x) = 4^x, describe the transformation to graph the function g(x) = 4^x + 1

• one unit down

• one unit left

• one unit up

• one unit right

Considering the function f(x) = 4^x, describe the transformation to graph the function g(x) = 4^x-2

• two units down

• two units left

• two units up

• two units right

Which of the following scenarios give reasonable interpretations of (1 + 0.05)^t in the expression 250(1 + 0.05)^t ?

Select all that apply.

• A sinkhole is 250 feet deep. Every year, it becomes 5% deeper. After t years, the sinkhole is (1 + 0.05)^t feet deeper.

• A snake is 250mm long. It increases in length by 5% every week. After t weeks the snake will be (1 + 0.05)^t longer.

• Marisa deposits $250 into a bank account that pays 5% interest compounded annually. After t years, she will have (1 + 0.05)^t dollars in the account.

• A cell culture has 250 cells, and the population of cells grows at a rate of 5% per day . There were (1 + 0.05)^t cells when the culture first started to grow.

The expression 3280(1.0117)^12t models the future population of wolves in a park after t years. Which of the following is the approximate yearly growth rate of the wolf population.

• 0.1%

• 1.17%

• 14.04%

• 14.98%

Suppose a culture of bacteria begins with 5000 cells and dies by 30% each year. Write an equation that represents this situation.

• y=5000(0.7)^x
• y=30(5000)^x
• y=5000(1.3)^x
• y=5000x^x