Change over Time Practice Problems Name: Per:
1. To help you save enough money to buy your first car, your parents open up a savings account for you at Bank of South Pasadena. This savings account earns 1.2% interest on the balance at the end of the month. Suppose that you saved up $1,500 from babysitting for your neighbor’s kids and tutoring math. You deposit the $1,500 into the account on January 1st.
a. If you don’t touch the money in the savings account, nor do you deposit any more money, how much money will be in the account at the end of the month? How much money will be there at the end of two months? Explain and show your work.
b. When will you have at least$2,000? Explain how you got your answer.
c. Suppose you take out $300 at the end of each month starting in January. How much will you have in the account at the end of January? How about at the end of February? Show and explain your work.
d. Under the conditions described in Part c and assuming you don’t deposit any more money into the account, after how many months will your account have no money left in it? Show and explain your work.
2. the annual change in the population of Mathvania depends on the population the previous year, the number of people born each year, the number of people who die each year and the number of people who move to or leave Mathvania each year. The statistics for Mathvania are given below.
Births every year will equal about 2.5% of the total population.
Deaths every year will equal about 0.3% of the population.
Every year approximately 0.01 million more people will leave Mathvania than will move to Mathvania.
The 2007 population of Mathvania was 64.5 million.
a. Calculate estimates for the population of Mathvania in 2008, 2009, 2010 and 2011.
Show your work:
Year / Population (in millions)2008
2009
2010
2011
b. Describe how you made your estimates in Part a.
c. Write a rule for finding out the next year’s population depending on the current year’s population.
d. When will the population first reach 80 million people?
e. Describe the pattern of change over time if the births every year increased to 3% of the population and everything else stayed the same.