Chapter 10 Sec 5 Exponential Functions

2 of 16 Algebra 1 Chapter 10 Sections 5 & 6 Power of 2 Which would desire most. 1.$1, 000, 000 in 30 days or… 2. 2 cents today then doubled for 30 days.

3 of 16 Algebra 1 Chapter 10 Sections 5 & 6 Power of = = = 20, = = = 41, = = = 83, = = = 167, = = = 335, = = = 671, = = 1, = 1,342, = = 2, = 2,684, = = 5, = 5,368, = = 10, = 10,737,418.24

4 of 16 Algebra 1 Chapter 10 Sections 5 & 6 Exponential Function From the previous example we can see, to find the amount of money accumulated, y, over x amount of days can be written as: y = 2 x. This type of function, in which the variable is the exponent, is called an exponential function.

5 of 16 Algebra 1 Chapter 10 Sections 5 & 6 Graph an exponential Function with a >1 a. Graph y = 4 x. State the y-intercept x 4x4x4x4xy / / b. Use graph to find approximate value of ~

6 of 16 Algebra 1 Chapter 10 Sections 5 & 6 Graph an exponential Function with 0 < a < 1 a. Graph. State the y-intercept x (1/2) X y -3 (1/2) (1/2) (1/2) (1/2) 0 1 1(1/2) 1 1/2 2(1/2) 2 1/4 b. Use graph to find approx value of (1/2) -2.5 (1/2) -2.5 ~

7 of 16 Algebra 1 Chapter 10 Sections 5 & 6 Identify Exponential Behavior Determine whether each set of data displays. Method 2. Graph the data. Method 1. Look for a pattern. The domain values are at regular intervals of 10. See if there is a common factor among the range Since the domain values are at regular intervals and the range have a common factor. The data is probably exponential, involving (1/2) x x y

8 of 16 Algebra 1 Chapter 10 Sections 5 & 6 Identify Exponential Behavior Determine whether each set of data displays. Method 2. Graph the data. Method 1. Look for a pattern. The domain values are at regular intervals of 10. The range values have a common difference 6. x y

Chapter 10 Sec 6 Exponential Growth/Decay

10 of 16 Algebra 1 Chapter 10 Sections 5 & 6 General Equation

11 of 16 Algebra 1 Chapter 10 Sections 5 & 6 Exponential Growth In 1971, there were 294,105 females participating in high school sports. Since then, that number has increased an average of 8.5% per year. a. Write an equation to represent the number of females participating in high school sports since y = C(1 + r) t y = 294,105( ) t y = 294,105(1.085) t y = 294,105(1.085) t b. How many female students participated in 2001? y = 294,105(1.085) t t = or 30 y = 294,105(1.085) t t = or 30 y = 294,105(1.085) 30 y = 294,105(1.085) 30 y ~ 3,399,340 y ~ 3,399,340

12 of 16 Algebra 1 Chapter 10 Sections 5 & 6 Compound interest The equation, where A is the amount of the investment, P is the principal (initial amount invested), r is the annual rate of interest expressed as a decimal, n is the number of times the interest is compounded each year, and t is the number of years the money is invested. Example: Use info on right. If money was invested at 6% per year compounded semiannually (2 times a year), How much money would there be in 2026? P = 24, r = 6% or 0.06, n = 2 t = = 400

13 of 16 Algebra 1 Chapter 10 Sections 5 & 6 General Equation

14 of 16 Algebra 1 Chapter 10 Sections 5 & 6 Exponential Decay In 1950, the use of coal by residential and commercial users was million tons. Because of cleaner fuels the use of coal has decreased by 6.6% per year a. Write an equation to represent the use of coal since y = C(1 - r) t y = 114.6( ) t y = 114.6(0.934) t b. Estimate the amount of coal that will be used in y = 114.6(0.934) t t = or 65 y = 114.6(0.934) 65 y ~ 1.35 million tons of coal.

15 of 16 Algebra 1 Chapter 10 Sections 5 & 6Depreciate Sometimes items decrease in value or depreciate. Cars, office equipment depreciate as they get older. You can use the exponential decay formula to determine the value of an item at a given time. A farmer buys a tractor for $50,000. If the tractor depreciates 10% per year, find the value of the tractor in 7 years. y = C(1 - r) t y = 50000( ) 7 y = 50000(0.90) 7 use a calculator… y ~ 23,914.85

16 of 16 Algebra 1 Chapter 10 Sections 5 & 6 Daily Assignment Chapter 10 Sections 5 & 6 Study Guide (SG) Pg 139 – 142 All