November 12, 2014
Objectives:
to write and apply exponential functions from two points
to recognize an equation from a set of points
create and solve doubling time and half life equations
1) Write an exponential function y = ab
x
whose
graph passes through (1,12) and (3, 108).
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2) Write an exponential function y = ab
x
whose
graph passes through(3,0.5) and (-4,64).
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3) An online store begins selling a new type of
basketball shoe. In week 2, 60 pairs of shoes were sold.
In week 4, the store sold 240 pair.
Write an exponential model (y = ab
x
)
that relates the number
of shoes (in pairs) sold to the week number.
How many did they originally sell?
What is the growth factor?
What is the % increase?
How many shoes (if the trend continues) will be
sold in week 6?
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Determine which ordered pairs are solutions to the given function.
4)
A) (0, -3) B) (2, -0.75) C) (-1, 6) D) (-2, -12)
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5) For your 16th birthday, you received $250
from your grandparents. (You have very nice
grandparents.) You plan to deposit this gift in
your savings account that earns 5% interest
compounded annually.
Write an equation in standard exponential form for the
amount in your account after x years.
How many years will take to double your money?
How much money will be in your account on your 18th
birthday given no deposits or withdrawals are made?
If your goal is to save this money to purchase a used car and
the car you have in mind costs $5210.99, how long will it take
to have enough money to make the purchase?
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Doubling Time: y = a(2)
x
d
Half Life: y = a( )
1
2
x
h
y: final amount after "x" events
a: initial amount
x: # of time intervals
d: doubling time
h: half life
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6) Suppose you have $475 invested in a bank. Your bank
advisor tells you to expect your money to double in about twelve
years.
When could you expect your bank balance to be $1000 if neither
deposits nor withdrawals are made?
Write an exponential equation to model the situation described .
Find the balance of your account after 3.5 years.
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7) A doctor's office did an audit on its paper usage. In an
effort to help the environment and reduce overhead cost, the
office wants to cut the amount of paper usage in half over
the next three years. They currently use 2250 reams of
paper per year.
Write an exponential equation to model the situation described.
How long will it take for the office staff to reduce their paper
usage to 2000 reams per year?
If the audit was completed in 2013 and the company could
realistically continue cutting their paper usage in half every
three years, how much paper will they be using in 2021.
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Assignment:
Worksheet #3
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