Unit 7: Exponents
Day 6: Problems involving Exponential
Growth and Decay
(doubling and half-life problems)
Today we will...
1. Continue to solve real-world problems involving
exponential relations
2. Learn how to recognize doubling and half-life problems
3. Create equations for doubling and half-life problems
and use these equations to solve for specific values
Review from Last Class:
In general,
y= a(b)x
b>1
Recall: r is the growth or
decay rate
(always as a decimal!)
0<b<1
y= a (1 + r)x
y= a (1 - r)x
Example
population of 8500 growing at
4% per year
Example
population of 35,421 decreasing at
9% per year
7-6 Exponential Growth and Decay
Doubling time
P = Po(2)t/d
P=
Po =
t=
d=
Half-life
M = Mo(1/2)t/h
M=
Mo =
t=
h=
Example 1
The population, P, of penguins in a certain area of
Antarctica can be modelled by the relation P = Po(2)t/90,
where t is the time, measured in months and Po is the
initial number of penguins.
a) What does the value of 90 represent in this formula?
b) If there were 800 penguins in the region today,
how many will there be in
i) 9 months?
ii) 2 years?
Example 2
The half-life of carbon-14 is 5730 years. The relation
C = (1/2)n/5730 is used to calculate the concentration, C,
in parts per trillion remaining n years after death.
Determine the carbon-14 concentration, rounded to
three decimal places, in:
a) a 5730 year old fossil
b) a 10 000 year old animal bone.
Applications of Exponential Growth and Decay
For each of the following, create an equation to model the situation:
1. 8 bacteria doubles every 7 days
2. 700 ml that has a half-life of 350 years
3. population of 8500 that decreases by 9.5% per month
4. value of $3400 that grows at 6% per year
Today's Practice Questions:
p. 410 #1, 3, 4, 6, 7, 10
Time
Amount (g)
0
1000
1 940 2
884 3 831 4 781 5
734 a) Write the equation for the exponential relation
b) Use the equation to determine the amount that will remain after 10 days.
c) When will there be 20 g remaining?