Modeling Exponential Functions

A website allows its users to submit and edit content in an online encyclopedia. The graph shows the number of articles a(t) in the encyclopedia months after the website goes live.

How many articles were in the encyclopedia when it went live?

• 0

• 30

• 60

• 180

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CCSS.HSF.LE.B.5

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

Tags

CCSS.HSF.LE.A.2

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

Tags

CCSS.HSF.LE.A.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

Tags

CCSS.HSF.LE.B.5

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

Tags

CCSS.HSF-LE.A.1A

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%

In a research experiment, the population of a colony of bacteria double every hour. The population, f(x), of the colony after x hours can be modeled by the function f(x) = 25(2)^x. What values for the domain are reasonable in the given context?

• all real numbers

• all real numbers greater than 0

• all real numbers greater than or equal to 0

• all real number greater than or equal to 25

The Miller family and the Adams family both purchased houses on the same day several years ago.

The Miller family bought their house for $159,352 and it has been increasing in value by 3.7% each year.

The value of the Adams family’s home since it was purchased, A(x) , can be modeled by the function A(x) = 142,809(1.04)^x, where x represents the number of years since the house was purchased.

Which family paid more for their house?

• The Miller family

• The Adams family

Tags

CCSS.8.F.A.2

CCSS.HSF.IF.C.9

The Miller family and the Adams family both purchased houses on the same day several years ago.

The Miller family bought their house for $159,352 and it has been increasing in value by 3.7% each year.

The value of the Adams family’s home since it was purchased, A(x) , can be modeled by the function A(x) = 142,809(1.04)^x, where x represents the number of years since the house was purchased.

Which family's home value is increasing at a faster rate?

• The Miller family

• The Adams family

Tags

CCSS.8.F.A.2

CCSS.HSF.IF.C.9

The growth of a population of bacteria can be modeled by the exponential function P(t) = 500(2)^t . The graph models the population of the bacteria colony P(t) as a function of the time, t , that has passed.

What is the average rate of change for the first 4 weeks of population growth?

• 2000 bacteria per week

• 2 bacteria per week

• 800 bacteria per week

• 1875 bacteria per week

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6