Unit 7: Exponents
Day 5: Modelling Exponential Growth and Decay
Today we will...
1. Create exponential equations for real-world growth and decay problems.
2. Use equations to graph and determine key values.
The graph below shows Evan's investment over a period of 30 years.
a) What amount of money did Evan initially invest?
b) How much is Evan's investment worth after 12 years?
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 800
1200 1600 2000 2400 2800 3200 3600 4000 4400 4800 5200 5600 6000
x y
Time (years)
Amount ($)
c) How long has Evan's money been invested if he has $4800?
A black fly population is modelled by the equation,
, where P is the population of black flies after t days.
b) What is the initial population?
c) What is the population at the end of the first week?
0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 1000
2000 3000 4000 5000 6000 7000 8000 9000 10000
x y
d) Approximately how long will it take for the population to be reduced by 50%?
a) Graph the relation.
t P
0 2 4 6 8 10
Example 2:
An exponential equation of the form y = a (b)
xcan be used to model real-world problems.
y = final value
a = initial value
b = growth or decay factor
« growth - (1 + rate of growth)
« decay - (1 - rate of decay)
ex. y = 1000(1.06)x is the equation for the graph in example 1.
Example 3:
The world population was 4.5 billion in 1980 and has increased at a rate of 2% per year since then.
a) Write an equation for this exponential relation.
c) Use your equation to predict the population in 2015.
b) What was the population in 1995?
d) When was the population 10.5 billion?
