- Sports In a single-elim ination to u rn a m e n t starting w ith 128 team s, half of the
rem aining team s are elim inated in each round.
a. Make a table, a scatter plot, an d a function rule to rep resen t th e situation.
b. Is it possible for 24 team s to rem ain after a round? W hich rep resen tatio n in
p art (a) m ade it the easiest to answ er th e question?
c. W hat is th e dom ain of th e function? W hat does th e do m ain represent?
d. How m any team s will be left after 5 rounds? - Car Value A family buys a car for $20,000. The value of th e car decreases about
20% each year. After 6 yr, th e family decides to sell th e car. Should they sell it for
$4000? Explain. - Think About a Plan You invest $100 a n d expect your m on ey to grow 8% each year.
About how m any years will it take for your investm ent to double?
- W hat function m odels th e grow th of your investm ent?
- How can you use a table to find th e approxim ate a m o u n t of tim e it takes for your
investment to double?- How can you use a graph to find th e approxim ate a m o u n t of tim e it takes for
your investment to double?
- How can you use a graph to find th e approxim ate a m o u n t of tim e it takes for
- Reasoning Give an exam ple of an exponential function in th e form y = a • bx
th at is n e ith e r an exponential grow th function n o r an exponential decay function.
Explain your reasoning.
State whether each graph shows an exponential growth function, an
exponential decay function, or neither.
- Use a table an d a scatter p lot to answ er each question.
a. You play a game of m usical chairs in which 32 players start an d you remove
2 chairs in each round. How m any rou n d s will you play before two players are left?
b. In a n o th er gam e of m usical chairs, you take away half of th e chairs each time.
If th e gam e begins w ith 32 players, how m any rounds will it take to get dow n to
two players?
c. Will a gam e w here you rem ove h a lf of th e chairs always en d m ore quickly th a n
one in w hich you take th e sam e n u m b e r of chairs each tim e? Give an example. - Business Suppose you start a law n-m ow ing business a n d m ake a profit of $400 in
th e first year. Each year, your profit increases 5%.
a. Write a function th a t m odels your an n u a l profit.
b. If you con tin u e your business for 10 yr, w hat will your total p ro fit be?
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PowerAlgebra.com “ Lesson 7-7 Exponential Growth and Decay 465