In this lesson, we will learn how to solve real-world problems involving exponential functions.

Students will be able to

Q1:

A microorganism reproduces by binary fission, where every hour each cell divides into two cells. Given that there were 15,141 cells to begin with, determine how many cells there were after 5 hours.

Q2:

A start-up company noticed that the number of those who use its product doubles every month. This month, they had 4,000 users. Assuming this trend continues, write an equation that can be used to calculate π(π), the number of users in π monthsβ time.

Q3:

The US Census is taken every ten years. The population of Texas was 3.05 million in 1900 and 20.9 million in 2000. By modeling the population growth as exponential, answer the following questions.

Write an exponential function in the form π(π)=ππο¦ο½ to model the population of Texas, in millions, π decades after 1900. Round your value of π to three decimal places.

According to the model, what was the population of Texas in 1950? Give your answer in millions to two decimal places.

Using the value of π from part 1, rewrite your function in the form π(π¦)=π(π)ο¦ο, where π¦ is the time in years after the year 1900. Round your value of π to four decimal places.

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