SECTION 7-6 : EXPONENTIAL FUNCTIONS ALGEBRA I @ SECTION 7-6 : EXPONENTIAL FUNCTIONS

1) Hey, try this with your parents 1) Hey, try this with your parents. In exchange for cleaning your room daily, they will give you 1¢ today, 2¢ tomorrow, 4¢ the next, and so on. How much money will your parents have to give you on day 30 if today is day zero? ANSWER : $10,737,418.24

EXPONENTIAL FUNCTION : is of the form The previous problem is an example of an exponential function. EXPONENTIAL FUNCTION : is of the form y = abx where a ≠ 0 and b > 0 and b ≠ 1. Examples :

Does the table or rule represent a linear or an exponential function Does the table or rule represent a linear or an exponential function? Explain. 2) x 1 2 3 y 6 18 54 4) y = -2x + 5 ANSWER : linear, slope-intercept form ANSWER : exponential, x3 3) 5) y = -2 • 5x x 1 3 5 7 y 2 8 11 ANSWER : exponential, in exponential form ANSWER : linear, +2 for x’s, +3 for y’s

6) Suppose a culture of bacteria doubles every hour 6) Suppose a culture of bacteria doubles every hour. There are initially 2200 bacteria and the function f(x) = 2200 • 2x models the problem. How many bacteria would you expect in the culture after 5 hours? ANSWER : 70,400

7) f(x) = 3 • 2x for x = 3 8) g(x) = -5 • (0.3)x for x = 2 Evaluate each function for the given value. 7) f(x) = 3 • 2x for x = 3 ANSWER : 24 8) g(x) = -5 • (0.3)x for x = 2 ANSWER : -0.45

9) Graph y = 2x

10) Graph.

Graphs of exponential functions : y = 3 • 2x y = -3 • 2x y = (1/2)x y = (-1/2)x

ALGEBRA I - SECTION 7-6 (Exponential Functions) 11/10/2018 ALGEBRA I - SECTION 7-6 (Exponential Functions)