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4.1 Exponential Growth Functions

4.1 Exponential 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 = ab x , where a = 0 and the base b is a positive number other than 1.

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4.1 Exponential Growth Functions

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  1. 4.1Exponential Growth Functions Retesting Opportunity: Dec. 1 4.1-4.2 Quiz: Dec. 3 Performance Exam: Dec. 4

  2. 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!

  3. Graph of y = 2x The graph y = 2x approaches the x-axis but never reaches it…we call the x-axis an asymptote

  4. Example 1: • Graph y = 5x

  5. Example 2: • Graph y = (-1/4)•2x

  6. Example 3: • Graph y = 3 • 2x+1 + 2 • Let’s look at y = 3•2x first

  7. 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.

  8. 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.

  9. 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

  10. 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

  11. 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.

  12. Example 5: • You deposit $3000 in an account that pays 6% interest compounded annually. In about how many years will the balance double?

  13. Homework: • P. 132 #1-15odd

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