Transcript Let`s review recursive formulas.

Section 5-1
Today, we will apply exponential
functions to solve problems.
Do you remember recursive formulas?
Because you will need to use them!
Let’s review recursive formulas.
u0  16
y-intercept
un  (1  .25)un 1
Growth rate
Percent change
Write an equation for the recursive formula.
u0  16
Remember from
yesterday:
un  (1  .25)un 1
f(x) = abx
f ( x)  16(.75)
x
Find the first three terms of the recursive
formula
u0  16
un  (1  .25)un 1
0
16
1
2
3
Evaluate the following equation at x = 0, x = 1, x = 2, and x = 3.
f ( x)  16(.75)
x
f(x)
0
1
2
x
3
p240 #2b, #3a
2b. 24, 36, 54
f ( x)  24(1.5) x
3a. f(0) = 125, f(1) = 75, f(2) = 45
u0  125
u1  (.6)un 1
How do you determine
percent increase or decrease?
2nd # - 1st #
1st #
p240 #4 all – just find percent change
4a. 25% decrease
4b. 33 1/3 % increase
4c. 6% decrease
4d. 6.38% increase
In 1991, the
population of the
People’s Republic
of China was
1.151 billion, with
a growth rate of
1.5% annually.
Write a recursive formula to model
this growth.
u0  1.151
un  (1  .015)un 1
Complete a table recording the
populations for the years 1991-2000.
Year
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
Pop.
1.151 1.168 1.186 1.204 1.222 1.240 1.259 1.277 1.297 1.316
Define the variables and write an exponential equation that
models this growth. Choose two table points and see if it works.
Define variables
Check
(1992, 1.168)
Independent (x) =
Dependent (y) =
YEAR
POPULATION
Write an equation
1.168 = 1.151(1.015)1
(2000, 1.316)
1.316 = 1.151(1.015)9
f(x) =
1.151(1.015)x


Work with your partner to complete #6
on p241 skip e.
Here are some hints to help you out:
a. You need to find the percent
change.
b. What should your exponent be if a
whole day starts at 8:00 am and he
is measuring at 8:00 pm?
c. What should your exponent be if
you are measuring at 12:00 noon?
d. If the plant starts at 2.56 cm tall,
how tall will it be when it doubles?
Guess and check to find the
exponent that gives you this
height.