exponential word problems · 4/25/2014 · 6% 2. 0.010% jan 223:47 pm 10.6 exponential word...
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WarmUpChange the following percents to decimals.
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.
1. 6% 2. 0.010%
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10.6 Exponential Word Problems
Benchmark: B.12 Apply real world
Goals: To use exponential equations in realword situations.
to exponential equations.applications
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Exponential Word Problems
• x is always time
• To write an exponential equation in word
• The rate is either
problems, use the form
(1 + %) if increasing (growth) (1 %) if decreasing (decay) double, triple, quadruple,... (growth) half, third, etc.,....(decay)
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Finding the RATE
• Look for percents or words that represent
• Identify if it is growth or decay
change, use the form
(1 + %) if there is a percent growth (1 %) if there is a percent decay
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Exponential Word Problems
• Read the question carefully.
• If an equation (function) is missing, write one. • Underline what you are looking for.
• Use the function to find the answer. • Does your answer make sense? Check units.
**You may need to find the rate first!**
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Example 1
1. Mr. Clark told his English class that each
vocabulary words they learned the previousweek students tend to forget one sixth of the
week. If the students learn 30 words, write an exponential equation to describe the numberof words forgotten after x weeks.
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Example 2
2. The median household income in the US
between 1979 and 1999. If the median increased by an average of 0.5% each month
household income was $37,060 in 1979, write an equation for the median householdincome for t months.
What was the median household income inafter 5 years?
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Example 4
4. In 1971, there were 294,105 females
that number has tripled each year. Write anparticipating in high school sports. Since then,
equation to represent the number of females participating in high school sports since 1971.How many females would be participatingtoday if the trend continued?
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Example 5
5. Your family bought a house 10 year ago.
your neighborhood has declined 3% per Since that time, the value of the real estate in
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?
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Example 6
6. In math class, if you do not do your
from that day. We complete 160 topicshomework you will only learn 1/4th of the 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?
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Using Exponential Functions
7. The amount of money spent at the Cherry
in millions of dollars can be estimated by theHill Mall continues to increase. The total T(x)
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.
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Using Exponential Functions
8. Suppose a rabbit population of 10 rabbits
rule and evaluation function for how many quadroupled every 2 months. Write a function
rabbits will exist after 2 years?
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Example 9
9. You invest $200 when you turn 18 years
every four years. How much money will you old. You are told your money will double
have when you are 42 years old?
EXPLAIN!
If it doubles every 6 years instead of every 4,how would your investment worth change?
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Compound Interest
Compound Interest Formula
A = Amount of invested at the ENDP = Principal (initial amount) r = Annual rate of interest n = number of times compounded per year t = number of years
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Compound Vocabulary
Compound Interest Formula
Annual once a yearSemiannually twice a yearQuarterly four times a yearMonthly 12 times a year Weekly 52 times a year Daily 365 times a year
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Example 10
10. Karen has $1000 that she invests into an
quarterly. How much money does Karen account that pays 3.5% interest compounded
have at the end of 5 years?
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Example 11
11. You decided to put $100 into a bank
interest rate of 2% compounded monthly. account. You are told you will get an annual
How much money will you have after 10 years?
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Example 12
12. You decided to put $100 into a bank
interest rate of 2% compounded monthly. account. You are told you will get an annual
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?
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Example 13
13. Instead of putting your $100 in the bank
Market). The mutual fund gets an average you decide to put it in a mutual fund (Stock
annual return of 7% compounded monthly.How much money will you have after 10years?
Would you rather invest with a bank or stockmarket? Explain.
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I You a Question
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!
Exponential Word Problems
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Almost Finished...
Take out your agenda copy down due datesStandard Checks
Homework
Do NOT pack up until you are told to do so!
Tests
Apr 2110:19 PM