Transcript 6.1 Exponential Growth and Decay

6.1 Exponential Growth and Decay
Learning Objective: To determine the multiplier for exponential growth and
decay, and to write and evaluate expressions to model growth and decay
situations.
Warm-up (IN)
Learning Objective: To determine the multiplier for exponential growth and decay, and to
write and evaluate expressions to model growth and decay situations.
.
Notes
Exponential Function multiplier
y  C (1  r )
Final
amount
Initial
amount
t
time
rate
the percent written
as a decimal
multiplier
Growth -
1 r
Decay -
1 r
Learning Objective: To determine the multiplier for exponential growth and decay, and to
write and evaluate expressions to model growth and decay situations.
Ex 1 – Find the multiplier for each rate of growth or decay.
a. 9% growth
1 r
1  .09
1.09
b. 12% decay
1 r
1  .12
.88
Ex 2 – Evaluate each expression for the given value of x.
1
a. 70.5 for x 
2
1
70.5 2
x
4.95
b. 122 for x  6.5
6.52
122
x 2
271 .53
Learning Objective: To determine the multiplier for exponential growth and decay, and to
write and evaluate expressions to model growth and decay situations.
EX 3 – An experiment starts with 100 bacteria and
doubles every hour. Write a model for the # of bacteria
and find the # after 8 hours.
y  100 1  1
y  100 1  1
y  1002

8

t
t
y  25,600
EX 4 – You start a savings account with $1000 that pays
6.5% interest compounded yearly. What is the balance
after 5 years?
5
y  1000 1 .065 
y  1370.09
Learning Objective: To determine the multiplier for exponential growth and decay, and to
write and evaluate expressions to model growth and decay situations.
EX 5 – You bought a car for $18,000 in 2010. The value of
the car depreciates by 19% each year. Write an
exponential decay model and find the value of the car in
2012.
t
y  18000 1  .19 
y  18000 .81
2
.81
y  18000  
y  $11,809
t
Out – Describe the difference between the
procedures for finding the multiplier for a
growth rate of 5% and a decay rate of 5%.
Summary – Now,
I can figure out…
HW –