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4.1Exponential Growth Functions
Retesting Opportunity: Dec. 1
4.1-4.2 Quiz: Dec. 3
Performance Exam: Dec. 4
Vocabulary An exponential function has the form
y = abx, where a = 0 and the base b is a positive number other than 1.
If b > 1, then the function y = abx is an exponential growth function, and b is called the growth factor.
An asymptote is a line that a graph approaches more and more closely…but NEVER touches!
Graph of y = 2x
The graph y = 2x
approaches the x-axis but never reaches it…we call the x-axis an asymptote
Example 1: Graph y = 5x
Example 2: Graph y = (-1/4)•2x
Example 3: Graph y = 3 • 2x+1 + 2
Let’s look at
y = 3•2x first
Vocabulary Exponential Growth Model
When a real-life quantity increases by a fixed percent each year (or other time period), the amount y of the quantity after t years can be modeled by the equation y = a(1 + r)t, where a is the initial amount and r is the percent increase expressed as a decimal.
Note that quantity 1 + r is the growth factor.
Example 4: The population of the United States was
248,718,301 in 1990 and was projected to grow at a rate of about 8% per decade.
Predict the population, to the nearest hundred thousand, for the year 2010.
Solution: To obtain the growth factor for exponential
growth, add the growth rate to 100%. What is our growth factor?? Write the expression for the population t
decades after 1990.
248,718,301·(1.08)t
108% or 1.08
Solution continued: How many decades is it from 1990 to 2010?
2 decades We substitute 2 in for t and solve…
The predicted population for 2010 is
290, 100, 000
Compound Interest Formula The total amount of an investment, A, earning
compound interest is:
where P is the principle (starting amount), r is the interest rate, n is the number of times interest is compounded per year, and t is the time in years.
)(
1)(tn
n
rPtA
Example 5: You deposit $3000 in an account that pays 6%
interest compounded annually. In about how many years will the balance double?
)(
1)(tn
n
rPtA
Homework: P. 132 #1-15odd
