Homework Quiz

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Homework Quiz
Solve the equation.
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Notes
Exponential Growth
y Final amount a Initial amount b growth
factor x Length of growth (days, minutes, etc.)
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Discussion
Sally starts a chain email that requires each
recipient to pass it on to five new people after
24 hours else they be cursed with a lifetime of
bad-hair days. Sally sends the email to three of
her friends. If everyone who gets the email
obeys and sends it on to five people, how many
people will receive the email on the 15th day
after it started?
Initial amount 3 Growth Factor 5 Length of
Growth 15 Final amount y
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Notes
If the growth is given as a rate in percent, it
must be converted to the growth factor by first
changing it to a decimal, then adding
1. Example Growth rate 32 Growth factor 1.32
Growth Rate
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Discussion
Two grey squirrels stow away on a freight ship
heading for Greenland. When they arrive, they
take to their new environment and begin to
thrive. Their population grows at a rate of 45
per month. How many squirrels will there be
after one and a half years?
Initial amount 2 Growth rate 45 Growth factor
1.45 Length of Growth 18 months Final amount y
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Notes
Exponential Decay
y Final amount a Initial amount b decay
factor x Length of decay (days, minutes, etc.)
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Discussion
A sheet of paper with an area of 93.5 square
inches is folded in half 7 times. What is the
area of the paper after the last fold?
Initial amount 93.5 Decay Factor ½ Length of
Decay 7 Final amount y
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Notes
If the decay is given as a rate in percent, it
must be converted to the decay factor by changing
it to a decimal and subtracting it from
1. Example Decay Rate 12 Decay Factor 0.88
Decay Rate
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Discussion
You purchase a brand new 2007 BMW for 45,000.00.
Each year the value of a car depreciates about
15. How much is your BMW worth in the year 2020?
Initial amount 45,000 Decay Rate 15 Decay
Factor 0.85 Length of Decay 13 Final amount y
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Discussion
You deposit 100.00 into a savings account with a
5 annual interest rate. How much money is in
the account after 10 years?
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Discussion
Most savings accounts pay interest on the amount
more than once a year. If the bank deposits the
amount of interest earned into the account every
month (compounded monthly), how much money would
be in that account after 10 years?
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Notes
Compound Interest
A Final Amount of Investment P Principle
(Initial value of investment) r Annual Interest
Rate n Number of times interest is compounded t
Time in years
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Notes
Compound Interest
Compounded n
Annually 1
Semiannually 2
Quarterly 4
Monthly 12
Weekly 52
Daily 365
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Discussion
How much money would be in that account after 10
years if the interest is compounded daily?
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Notes
If you are given a problem with exponential
growth or decay, and are asked to find the
initial amount or the amount of time, you must
first write the equation, then solve for the
missing value.
Exponential Models
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Discussion
The value of a house is increasing at a rate of
12 per year, it is now worth 200,000. After
how many years will it be worth 500,000?
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Discussion
You invest 5000 in the bank at 5 interest
calculated continuously. How much will you have
after 6 years?
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Class Work
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