P.o.D. – The population N of a certain bacteria grows according to
the equation 𝑁 = 200 ∙ 21.4𝑡 , where t is the time in hours.
1.) How many bacteria were present at the beginning of the
experiment?
2.) After how many hours will the number of bacteria double?
3.) Estimate the number of bacteria in 10 hours.
4.) Estimate the number of bacteria 2 hours before the
experiment started.
9-2: Exponential Decay
Learning Target: I will be able to recognize properties of
exponential functions; create and apply exponential decay
models; graph exponential functions.
Depreciation – the ____ in value of an object over time. _______
depreciate in value as an example.
Recall, exponential growth is modeled by ______________________.
EX: Suppose a new piano costs $8,500 and depreciates 6% each
year.
a.)
Write an equation that gives the piano’s value when it
is t years old.
b.)
Predict the piano’s value when it is 5 years old.
Read “Half-Life and Radioactive Decay” on the top of page 588.
EX: Strontium 90 ( 90𝑆𝑟) has a half life of 29 years. This means that
in each 29-year period, half of the Strontium decays and half
remains. Suppose you have 1000 grams of Strontium.
a.)
How many grams of Strontium remain after 6 half-life
periods?
b.)
How many years is 6 half-life periods?
c.)
Write a recursive formula for 𝑎𝑛 , the number of grams
of Strontium that remain after n half-life periods.
d.)
Write an explicit formula for 𝑎𝑛 .
Do we understand the difference between exponential growth
and decay?
EX: Suppose a sample began with 80% pure carbon-14, which has
a half-life of 5730 years.
a.)
Write an equation for the percent of carbon-14
remaining in the original sample after x half-life
periods?
b.)
Graph your equation from part a and use it to find the
age of the sample when it contains 60% of its original
carbon-14.
Determine whether each of the following models represents
growth or decay:
a.)
𝑦 = 0.98𝑥 b.) 𝑦 = (1.92)𝑥
c.)𝑦 = 120(0.2)2
EX: Morgan buys a car for $18,000. If the value decreases by 12%
per year:
a.)
Write a formula for the value A of the car, t years after
they buy it.
b.)
Find the value of the car after 5 years.
EX: Strontium has a half-life of 29 years. Suppose you have an
initial sample of 100 grams.
a.)
How much will be left after five half-lives?
b.) How much will be left after 100 years?
HW Pg.591
Worksheet 9.2
4-14