Videos and solutions to help Algebra I students learn how to compare linear and exponential models of population growth.

New York State Common Core Math Module 3, Algebra I, Lesson 6

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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.

1. A savings account accumulates no interest but receives a deposit of $825 per month.

2. A house is purchased for $400,000. The value of a house increases by 1.5% per year.

3. A game farm has 5 alligators. Every year, the alligator population is 9/7 of the previous year’s population.

1. Student Friendly Bank pays a simple interest rate of 2.5% per year. Neighborhood Bank pays a compound interest rate of 2.1% per year, compounded monthly.

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?

2. The table below represents the population of the state of New York for the years 11800–2000. Use this information to answer the questions.

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?

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