6.1 Exponential Growth and Decay Functions Warm up

Size: px

Start display at page:

Download "6.1 Exponential Growth and Decay Functions Warm up"

Sheila Simpson
6 years ago
Views:

15%? 8. Your Lester's bill is $P. 15%? 9.

1 6.1 Exponential Growth and Decay Functions Warm up Simplify the expression Your Lester's bill is $14. How much do you owe your server if you tip 15%? 8. Your Lester's bill is $P. How much do you owe your server if you tip 15%? 9. A new car loses 11% of its value the moment it leaves the lot. After 5 years, it depreciates 63%! A new car costs $C. a)what is its worth as it leaves the lot? b)what is its worth in 5 years?

2 Complete the table and graph. 1. y = 3x 2. y = 2 x 3. y = 2(2) x 4. #2 and #3 are examples of exponential functions. Describe what makes a function exponential. 5. Describe the transformation from #2 to #3.

6.1 Exponential Growth and Decay Functions What are some of the characteristics

a) Match each exponential function with its graph.

c) Determine the domain, range, and y-intercept of the graph of f (x) = b x,

3 6.1 Exponential Growth and Decay Functions What are some of the characteristics of the graph of an exponential function? a) Match each exponential function with its graph. b) Use a table of values to sketch the graph of the function, if necessary. c) Determine the domain, range, and y-intercept of the graph of f (x) = b x, where b is a positive real number other than 1. d) Explain your reasoning. 1. f (x) = 2 x 2. f (x) = 3 x 3. f (x) = 4 x 4. f (x) = 5. f (x) = 6. f (x) =

4 Tell whether each function represents exponential growth or exponential decay. Then sketch the function. 1. y = 2 x 2. y = 3. y = 4 x 4. y = 5. f (x) = (0.25) x 6. f (x) = (1.5) x What would the asymptote be for y = 4 + 2? x What would the y-intercept be?

5 General Exponential Model (Growth rate not given as a percent) amount after time, t y = ab t initial amount growth/decay rate # of time periods 7. The value of a car y (in thousands of dollars) can be approximated by the model y = 25(0.85) t, where t is the number of years since the car was new. a. Tell whether the model represents exponential growth or exponential decay. b. Identify the annual percent increase or decrease in the value of the car. c. Estimate when the value of the car will be $8000. (Hint: Use the trace or table feature of the graphing calculator to determine to value of t when y = 8) 8. What if the value of the car can be approximated by the model y = 25(0.9) t. a. Identify the annual percent decrease in the value of the car. b. Estimate when the value of the car will be $8000.

6 General Exponential Model (Growth rate given as a percent) amount after time, t y = a(1 + r) t initial amount growth/decay factor % increase or decrease # of time periods 9. In 2000, the world population was about 6.09 billion. During the next 13 years, the world population increased by about 1.18% each year. a. Write an exponential growth model giving the population y (in billions) t years after b. Estimate the world population in c. Estimate the year when the world population was 7 billion. (Use table or trace feature of graphing calculator) 10. What if the world population increased by 1.5% each year. a. Write an equation to model this situation. b. Estimate the year when the world population was 7 billion.

7 Half-Life Model y = a(0.5) initial amount t half-life 11. The half-life of a radioactive kind of iron is 45 days. If you start with 1,192 grams of it, how much will be left after 90 days? 12. You have 5,952 grams of a radioactive kind of xenon. How much will be left after 56 minutes if its half-life is 14 minutes? 13. The amount y (in grams) of the radioactive isotope chromium-51 remaining after t days is y = a(0.5) t/28, where a is the initial amount (in grams). a. What is the half life of chromium-51? b. What percent of the chromium-51 decays each day? 14. The amount y (in grams) of the radioactive isotope iodine-123 remaining after t hours is y = a(0.5) t/13, where a is the initial amount (in grams). What percent of the iodine-123 decays each hour?

The amount of money A that a principal P will grow after t years at an interest rate r (in decimal form), compounded n times a year is given by the formula: 6.

8 The amount of money A that a principal P will grow after t years at an interest rate r (in decimal form), compounded n times a year is given by the formula: 6.1 Notes Compound Interest Formula Label the formula. if compounded: n = monthly quarterly semiannually daily 15. You deposit $9000 in an account that pays 1.46% annual interest. Find the balance after 3 years when the interest is compounded quarterly. 16. In Example 15, find the balance after 3 years when the interest is compounded daily.

EXPONENTIAL FUNCTIONS GET A GUIDED NOTES SHEET FROM THE BACK!

EXPONENTIAL FUNCTIONS GET A GUIDED NOTES SHEET FROM THE BACK! EXPONENTIAL FUNCTIONS An exponential function is a function with a variable in the exponent. f(x) = a(b) x EXPONENTIAL FUNCTIONS Parent graphs