Identify each variable in an exponential growth model and say what it represents.
Only looking at an equation, how would you determine if the function represents a growth model or a decay model?
Also, copy the equation into your notebook for class and have each variable labeled to be ready for class.
Given the scenario below, use the equation to find p(2) and explain in complete sentences what you have just determined in the context of the situation.
The population of Jacksonville was 3,810 in 2007, and is growing at an annual rate of 3.5%. The population of Jacksonville can be modeled by the function P(t) = 3810(1.035)^t.
3,810 is the initial amount 2007(0) is the time exponent 3.5 anual rate - 0.035
Base is > than 1 its exponential growth Base is < than 1 its exponential decay
P(2) : 4081.36 is the population in the year 2009
8.2:
Look at the graph below. Both exponential growth models represent two different bank accounts.
The blue exponential growth model represents a bank account where a person deposited $1000 with a $50 bonus for signing up. The account has a 4.99% interest rate and the interest is compounded annually.
The red exponential growth model represents a bank account where a person deposited $1000. The account has a 5.99% interest rate and the interest is compounded monthly.
chapter_8_bank_accounts.jpg
Compare and contrast the two bank accounts in your online journal by answering the following questions:
Write a function that represents the red exponential growth model.
What is the y-intercept of each function? Explain in the context of the situation.
Which account is better? Is this always true? Be specific, using dates and account values from the graph to support your argument.
Which account would you choose when opening to save up for your college in a few years and why?
Would you choose that same account to start your child's college fund (if you had a child) and why?
1. 1000(1+.0599)^t 2. The y-intercept is the initial amount and for Blue is (0,10500) and Red (0,1000) 3.The red account is better but this is not always true because when the x value is 0 the y value is only 1000. However, in the blue account when x is 0 y is 10500 which is $500 more than the amount in the red account. 4. The Red account because it is better long term. 5. Yes, I would because it is much more benificial long term.
8.1:
In your online journal:Given the scenario below, use the equation to find p(2) and explain in complete sentences what you have just determined in the context of the situation.
The population of Jacksonville was 3,810 in 2007, and is growing at an annual rate of 3.5%. The population of Jacksonville can be modeled by the function P(t) = 3810(1.035)^t.
3,810 is the initial amount
2007(0) is the time exponent
3.5 anual rate - 0.035
Base is > than 1 its exponential growth
Base is < than 1 its exponential decay
P(2) : 4081.36 is the population in the year 2009
8.2:
Look at the graph below. Both exponential growth models represent two different bank accounts.The blue exponential growth model represents a bank account where a person deposited $1000 with a $50 bonus for signing up. The account has a 4.99% interest rate and the interest is compounded annually.
The red exponential growth model represents a bank account where a person deposited $1000. The account has a 5.99% interest rate and the interest is compounded monthly.
Compare and contrast the two bank accounts in your online journal by answering the following questions:
1. 1000(1+.0599)^t
2. The y-intercept is the initial amount and for Blue is (0,10500) and Red (0,1000)
3.The red account is better but this is not always true because when the x value is 0 the y value is only 1000. However, in the blue account when x is 0 y is 10500 which is $500 more than the amount in the red account.
4. The Red account because it is better long term.
5. Yes, I would because it is much more benificial long term.