The Power of Exponential Growth
Videos to help Algebra I students learn how to model with and solve problems involving exponential formulas.
New York State Common Core Math Module 3, Algebra I, Lesson 5
Plans and Worksheets for Algebra I
Plans and Worksheets for all Grades
Lessons for Algebra I
Common Core For Algebra I
A typical thickness of toilet paper is inches. This seems pretty thin, right? Let’s see what happens when we start folding toilet paper.
a. How thick is the stack of toilet paper after 1 fold? After 2 folds? After 5 folds?
b. Write an explicit formula for the sequence that models the thickness of the folded toilet paper after n folds.
c. After how many folds will the stack of folded toilet paper pass the 1 foot mark?
d. The moon is about 249, 000 miles from Earth. Compare the thickness of the toilet paper folded 50 times to the distance from Earth.
How folding paper can get you to the moon?
Problem Set Sample Solutions
2. A three-bedroom house in Burbville was purchased for $190,000. If housing prices are expected to increase 1.8% annually in that town, write an explicit formula that models the price of the house in t years. Find the price of the house in 5 years.
4. The population growth rate of New York City has fluctuated tremendously in the last 200 years, the highest rate estimated at 126.8% in 1900. In 2001, the population of the city was 8,008,288, up 2.1% from 2000. If we assume that the annual population growth rate stayed at 2.1% from the year 2000 onward, in what year would we expect the population of New York City to have exceeded ten million people? Be sure to include the explicit formula you use to arrive at your answer.
5. In 2013, a research company found that smartphone shipments (units sold) were up 32.7% worldwide from 2012,
with an expectation for the trend to continue. If 959 million units were sold in 2013, how many smartphones can
be expected to be sold in 2018 at the same growth rate? (Include the explicit formula for the sequence that models
this growth.) Can this trend continue?
6. Two band mates have only 7 days to spread the word about their next performance. Jack thinks they can each pass 100 out fliers a day for 7 days and they will have done a good job in getting the news out. Meg has a different strategy. She tells 10 of her friends about the performance on the first day and asks each of her 10 friends to each tell a friend on the second day and then everyone who has heard about the concert to tell a friend on the third day and so on, for 7 days. Make an assumption that students make sure they are telling someone who has not already been told.
a. Over the first 7 days, Meg’s strategy will reach fewer people than Jack’s. Show that this is true.
b. If they had been given more than 7 days, would there be a day on which Meg’s strategy would begin to inform more people than Jack’s strategy? If not, explain why not. If so, which day would this occur on?
c. Knowing that she has only 7 days, how can Meg alter her strategy to reach more people than Jack does?
Chain emails are emails with a message suggesting you will have good luck if you forward the email on to others.
Suppose a student started a chain email by sending the message to 3 friends and asking those friends to each send the
same email to 3 more friends exactly 1 day after they received it.
a. Write an explicit formula for the sequence that models the number of people who will receive the email on the
day. (Let the first day be the day the original email was sent.) Assume everyone who receives the email
follows the directions.
b. Which day will be the first day that the number of people receiving the email exceeds 100?
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