These lessons, with videos, examples and step-by-step solutions, help Algebra I students learn how to compare linear and exponential models of population growth.
Related Pages
Exponential Growth & Decay
Lesson Plans and Worksheets for Algebra I
Lesson Plans and Worksheets for all Grades
More Lessons for Algebra I
Common Core For Algebra I
Compare Linear Growth and Exponential Growth
State whether each example is linear or exponential, and write an explicit formula for the sequence that models the growth for each case. Include a description of the variables you use.
A savings account accumulates no interest but receives a deposit of $825 per month.
A house is purchased for $400,000. The value of a house increases by 1.5% per year.
A game farm has 5 alligators. Every year, the alligator population is 9/7 of the previous year’s population.
Problem Set Sample Solutions
a. Which bank will provide the largest balance if you plan to invest $10,000 for 10 years? For 20 years?
b. Write an explicit formula for the sequence that models the balance of the Student Friendly Bank t years after a deposit is left in the account.
c. Write an explicit formula for the sequence that models the balance at the Neighborhood Bank balance m months after a deposit is left in the account.
d. Create a table of values indicating the balances in the two bank accounts from year 2 to year 20 in 2 year increments. Round each value to the nearest dollar.
e. Which bank is a better short-term investment? Which bank is better for those leaving money in for a longer period of time? When are the investments about the same?
f. What type of model is Student Friendly Bank? What is the rate or ratio of change?
g. What type of model is Neighborhood Bank? What is the rate or ratio of change?
a. Using the year 1800 as the base year, an explicit formula for the sequence that models the population of New York is P(t) = 300000(1.021)^{t}, where t is the number of years after 1800. Using this formula, calculate the projected population of New York in 2010.
b. Using the year 1900 as the base year, an explicit formula for the sequence that models the population of New York is P(t) = 7300000(1.0096)^{t}, where t is the number of years after 1900. Using this formula, calculate the projected population of New York in 2010.
c. Using the internet (or some other source), find the population of the state of New York according to the 2010 census. Which formula yielded a more accurate prediction of the 2010 population?
Try the free Mathway calculator and
problem solver below to practice various math topics. Try the given examples, or type in your own
problem and check your answer with the step-by-step explanations.
We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.