exponential function exponential growth asymptote growth factor exponential decay decay factor

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2 exponential function exponential growth asymptote growth factor exponential decay decay factor

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4 Answer: Graph Exponential Growth Functions Graph of y = 4 x. State the domain and range. Domain = {all real numbers} Range = {y y > 0}

5 Graph of y = 3 x. State the domain and range. A. B. C. D. Domain = {all real numbers} Range = {y y > 0} A. A B. B C. C D. D

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7 Graph Transformations A. Graph the function y = 3 x 2. State the domain and range. The equation represents a translation of the graph y = 3 x down 2 units.

8 Graph Transformations Answer: Domain = {all real numbers} Range = {y y > 2}

9 A. Graph the function y = 2 x 4. State the domain and range. A. B. The equation represents a translation of the graph y = 2 x down 4 units. C. D. Domain = {all real numbers} Range = {y y -3} A. A B. B C. C D. D

10 Graph Transformations B. Graph the function y = 2 x 1. State the domain and range. The equation represents a translation of the graph y = 2 x right 1 unit.

11 Graph Transformations Answer: Domain = {all real numbers} Range = {y y 0}

12 B. Graph the function y = 4 x State the domain and range. A. B. Domain = {all real numbers} Range = {y y 3} The equation represents a translation of the graph y = 4 x 2 units right and 3 units up. C. D. A. A B. C C. D

13 Graph Exponential Growth Functions INTERNET In 2006, there were 1,020,000,000 people worldwide using the Internet. At that time, the number of users was growing by 19.5% annually. Draw a graph showing how the number of users would grow from 2006 to 2016 if that rate continued. First, write an equation using a = (in billions), and r = y = 1.020(1.195) t Then graph the equation.

14 Answer: Graph Exponential Growth Functions

15 CELLULAR PHONES In 2006, there were about 2,000,000,000 people worldwide using cellular phones. At that time, the number of users was growing by 11% annually. Which graph shows how the number of users would grow from 2006 to 2014 if that rate continued? A. B. C. D. A B A. A B. B C. C 0% D. D 0% 0% 0% C D

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17 Graph Exponential Decay Functions A. Graph the function State the domain and range.

18 Graph Exponential Decay Functions Answer: Domain = {all real numbers} Range = {y y > 0}

19 Graph Exponential Decay Functions B. Graph the function State the domain and range. The equation represents a transformation of the graph of Examine each parameter. There is a negative sign in front of the function: The graph is reflected on the y-axis.

20 Graph Exponential Decay Functions h = 1: The graph is translated 1 unit right. k = 2: The graph is translated 2 units up. Answer: Domain = {all real numbers} Range = {y y < 2}

21 A. Graph the function A. B. C. D. A B A. A B. B C. C 0% D. D 0% 0% 0% C D

22 B. Graph the function State the domain and range. A. B. Domain = {all real numbers} Range = {y y < -3} C. D. Examine each parameter. There is a negative sign in front of the function: The graph is reflected on the y-axis. The graph is translated 2 units right. The graph is translated 3 units down. A. A B. B C. C D. D

23 Graph Exponential Decay Functions A. AIR PRESSURE The pressure of the atmosphere is 14.7 lb/in 2 at Earth s surface. It decreases by about 20% for each mile of altitude up to about 50 miles. Draw a graph to represent atmospheric pressure for altitude from 0 to 20 miles. y = a(1 r) t = 14.7(1 0.20) t = 14.7(0.80) t

24 Graph the equation. Graph Exponential Decay Functions Answer:

25 Graph Exponential Decay Functions B. AIR PRESSURE The pressure of the atmosphere is 14.7 lb/in 2 at Earth s surface. It decreases by about 20% for each mile of altitude up to about 50 miles. Estimate the atmospheric pressure at an altitude of 10 miles. y = 14.7(0.80) t Equation from part a. = 14.7(0.80) 10 Replace t with lb/in 2 Use a calculator. Answer: The atmospheric pressure at an altitude of about 10 miles will be approximately 1.6 lb/in 2.

26 A. AIR PRESSURE The pressure of a car tire with a bent rim is 34.7 lb/in 2 at the start of a road trip. It decreases by about 3% for each mile driven due to a leaky seal. Draw a graph to represent the air pressure for a trip from 0 to 40 miles. A. B. C. D. A. A B. B C. C 0% D. D 0% 0% 0% A B C D

27 B. AIR PRESSURE The pressure of a car tire with a bent rim is 34.7 lb/in 2 at the start of a road trip. It decreases by about 3% for each mile driven due to a leaky seal. Estimate the air pressure of the tire after 20 miles. A lb/in 2 B lb/in 2 C lb/in 2 A. A B. B C. C 0% D. D 0% 0% 0% A B C D D lb/in 2

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