Welcome!
[1] Take out your notebook
[2] Complete the warm up Given the sequence: 23.5, 34, 44.5, 55, ...
a) Find the Recursive Formula:
u0 = un = b) Explicit Formula:
un = c) Find the 12th term:
Unit 10 Day 7
Exponential Functions
• I can write an exponential function given
a starting value and growth rate.
• I can solve problems involving
exponential growth, decay and half­life
problems. 1
Exploration: Most cars depreciate as they get older. Originally a car cost $14,000 and it depreciates 1/5 of it's value every year. a) What is the car's value after 1 year?
b) What is the value after 2 years?
c) What is the value after n years?
Exponential Function:
(like the explicit form
of a geometric sequence)
f(x) = abx or f(x) = a(1 +/­ r)
x
Growth or Decay Factor
erase
Starting Value
(y-intercept)
percent change
2
ex 1)
f(x) = 250(.6)x
a) What is the starting value?
b) What is the growth/decay factor?
c) Write the recursive formula:
u0 = un = d) What is the value at x = 1 and x = 2? ex 2) This equation models the population of
a bacteria colony after t days
P(t) = 325(1+.35)t
a) How many bacteria does the colony start out with?
b) What is the growth/decay factor?
c) How many bacteria will there be after 8 days?
3
ex 3)
Record the first three terms then write an explicit formula.
uo = 12
un = .8un-1 for n≥1
x
ex 4) The function f(x) = 36(0.94)
gives the height of a snowman in inches
at every hour.
a) initial height? 36 in.
b) growth or decay factor? decay
c) percent of change? ­6%
d) find f(10): 19.3
find f(24): 8.15
e) real world meaning of f(24):
after 24 hours, the snowman is only 8.15 inches tall
4
x
ex 5) The function f(x) = 1(1.061)
gives the height of a giant sunflower
in inches.
a) initial height? 1 in.
b) growth or decay factor? growth
c) percent of change? +41%
d) find f(50): 19.3
find f(85): 153.4
e) real world meaning of f(85):
after 85 days of measuring, the sunflower is 153.4 inches tall (12' 7.4")
Homework:
Worksheet #7
5
Exit Quiz
1. Caitlynne puts $1000 into a bank account. The account gets 4%
interest annually. Write an exponential function for this situation.
How much money will she have after 4 years?
2. Write an exponential function from the recursive formula.
u0 = 45
un = 4un-1
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