Exponential Growth and Decay
Exponential growth and decay occurs when quantities increase or decrease proportional to the quantity present.
Ex. Growth Decay
Savings Accounts Radioactive Chemicals
RRSP’s Carbon Dating
Bacterial Cultures Value of a vehicle
Population Growth
Consider a city that’s population grows at 5% per year. In the year 2000 the population was 100 000.
2001 100 000 x 1.05 = 105 000
2002 105 000 x 1.05 = 110250
2003 110 250 x 1.05 = 115 763
n-years
The function that expresses the population after n years is .
Ex. A vase was purchased in 1990 for $8000. If the vase appreciates at 6% per year, how much:
a. Was it worth in the year 2000.
b. Will it be worth in the year 2030.
The standard form of an exponential growth or decay is .
is the initial amount.
b is the growth (1 + i) or decay (1- i) factor
i is the percent rate of growth or decay (as a decimal).
t is the number of growth or decay periods (this depends on the question)
Ex. The world population doubles every 35 years. If the population was 6 billion in 1999, find:
a. The population in 2050.
b. When the population will be 24 billion.
Sometimes, you will be asked to find the rate of increase of a population.
Ex. The population of a town was 24000 in 1980, and 29000 in 1990.
a. Determine an expression to find the population in t years after 1980.
b. What will be the population in 2020?
Exponential Decay
Ex. A car depreciates by 15% per year. If you buy a car for $15 000, find the value of the car in .
a) 3 years b) 10 years
Half-Life
Ex. An isotope of radium has a half-life of 1620 years. If you have 10mg, how much will be left in:
a) 50 years b) 500 years
Homework – Handout q. 1-5, 7, 8, 10, 12, 14, 15