244645229.notebook
April 25, 2014
WarmUp Change the following percents to decimals. 1. 6% 2. 0.010%
3. Rabbit populations increase by 34% each year. Find the rate of change.
4. Each day you forget 1/3 of the material you learn in science. Find the rate of change.
Jan 223:47 PM
10.6 Exponential Word Problems Benchmark: B.12 Apply real world applications to exponential equations.
Goals: To use exponential equations in real word situations.
Jan 223:47 PM
1
244645229.notebook
April 25, 2014
Exponential Word Problems • To write an exponential equation in word problems, use the form
• The rate is either (1 + %) if increasing (growth) (1 %) if decreasing (decay) double, triple, quadruple,... (growth)
half, third, etc.,....(decay) • x is always time Jan 223:47 PM
Finding the RATE • Look for percents or words that represent change, use the form
• Identify if it is growth or decay (1 + %) if there is a percent growth
(1 %) if there is a percent decay
Jan 223:47 PM
2
244645229.notebook
April 25, 2014
Exponential Word Problems • Read the question carefully. • Underline what you are looking for. • If an equation (function) is missing, write one. **You may need to find the rate first!** • Use the function to find the answer. • Does your answer make sense? Check units.
Jan 223:47 PM
Example 1 1. Mr. Clark told his English class that each week students tend to forget one sixth of the
vocabulary words they learned the previous week. If the students learn 30 words, write an
exponential equation to describe the number of words forgotten after x weeks.
Jan 223:47 PM
3
244645229.notebook
April 25, 2014
Example 2 2. The median household income in the US increased by an average of 0.5% each month
between 1979 and 1999. If the median household income was $37,060 in 1979, write an equation for the median household income for t months.
What was the median household income in after 5 years?
Jan 223:47 PM
Example 4 4. In 1971, there were 294,105 females participating in high school sports. Since then,
that number has tripled each year. Write an equation to represent the number of females participating in high school sports since 1971. How many females would be participating
today if the trend continued?
Jan 223:47 PM
4
244645229.notebook
April 25, 2014
Example 5 5. Your family bought a house 10 year ago. Since that time, the value of the real estate in
your neighborhood has declined 3% per year. If you initially paid $179,000 for their house, write an equation to model the value of your house after t years. How much would your house be worth today?
Jan 223:47 PM
Example 6 6. In math class, if you do not do your homework you will only learn 1/4th of the topics
from that day. We complete 160 topics during the course of the year. Write an equation that models how much you learn after x days.
If you don't do your homework, how many topics would learn after 3 weeks?
Jan 223:47 PM
5
244645229.notebook
April 25, 2014
Using Exponential Functions 7. The amount of money spent at the Cherry Hill Mall continues to increase. The total T(x)
in millions of dollars can be estimated by the function T(x)=12(1.12)x, where x is the number of years after the expansion in 2005. How much money is being spent in 2011? Round to the nearest tenth.
Jan 223:47 PM
Using Exponential Functions 8. Suppose a rabbit population of 10 rabbits quadroupled every 2 months. Write a function
rule and evaluation function for how many rabbits will exist after 2 years?
Jan 223:47 PM
6
244645229.notebook
April 25, 2014
Example 9 9. You invest $200 when you turn 18 years old. You are told your money will double
every four years. How much money will you have when you are 42 years old?
If it doubles every 6 years instead of every 4,
how would your investment worth change? EXPLAIN!
Jan 223:47 PM
Compound Interest Compound Interest Formula
A = Amount of invested at the END P = Principal (initial amount) r = Annual rate of interest
n = number of times compounded per year
t = number of years
Jan 223:47 PM
7
244645229.notebook
April 25, 2014
Compound Vocabulary Compound Interest Formula
Annual once a year Semiannually twice a year Quarterly four times a year Monthly 12 times a year Weekly 52 times a year Daily 365 times a year
Jan 223:47 PM
Example 10 10. Karen has $1000 that she invests into an account that pays 3.5% interest compounded
quarterly. How much money does Karen have at the end of 5 years?
Jan 223:47 PM
8
244645229.notebook
April 25, 2014
Example 11 11. You decided to put $100 into a bank account. You are told you will get an annual
interest rate of 2% compounded monthly. How much money will you have after 10 years?
Jan 223:47 PM
Example 12 12. You decided to put $100 into a bank account. You are told you will get an annual
interest rate of 2% compounded monthly. How much money will you have after 10 years?
Should you invest in an account compounded daily or monthly if they are
offering the same interest rate?
Jan 223:47 PM
9
244645229.notebook
April 25, 2014
Example 13 13. Instead of putting your $100 in the bank you decide to put it in a mutual fund (Stock
Market). The mutual fund gets an average annual return of 7% compounded monthly.
How much money will you have after 10 years?
Would you rather invest with a bank or stock market? Explain.
Jan 223:47 PM
I
You a Question Exponential Word Problems
Please solve the questions on your Ticket Out the Door. On the back how did you do today? Green I can do this! This is easy! Yellow I'm getting there. Red I need help!
Jan 223:47 PM
10
244645229.notebook
April 25, 2014
Almost Finished... Take out your agenda copy down due dates Standard Checks
Tests Homework
Do NOT pack up until you are told to do so!
Jan 223:47 PM
Apr 2110:19 PM
11
