Unit 8-1: Graphing Exponential Functions

Then/Now Graph exponential growth functions. Graph exponential decay functions.

Vocabulary exponential function exponential growth asymptote growth factor exponential decay decay factor

Concept (Pg. 451)

Example Graph y = 4x. State the domain and range. Graph Exponential Growth Functions Graph y = 4x. State the domain and range. Make a table of values. Connect the points to sketch a smooth curve.

Example Graph Exponential Growth Functions Answer: The domain is all real numbers, and the range is all positive real numbers.

Concept (pg. 452)

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

Example Answer: Domain = {all real numbers} Range = {y│y > –2} Graph Transformations Answer: Domain = {all real numbers} Range = {y│y > –2}

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

Example Answer: Domain = {all real numbers} Range = {y │y ≥ 0} Graph Transformations Answer: Domain = {all real numbers} Range = {y │y ≥ 0}

Example 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 = 1.020 (in billions), and r = 0.195. y = 1.020(1.195)t Then graph the equation.

Example Graph Exponential Growth Functions Answer:

Concept (pg. 453)

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

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

Example B. Graph the function State the domain and range. 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 in the x-axis. ● a = 4: The graph is stretched vertically.

Example ● h = 1: The graph is translated 1 unit right. 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}

Example Graph Exponential Decay Functions A. AIR PRESSURE The pressure of the atmosphere is 14.7 lb/in2 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

Example Graph Exponential Decay Functions Graph the equation. Answer:

Example Graph Exponential Decay Functions B. AIR PRESSURE The pressure of the atmosphere is 14.7 lb/in2 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 10. ≈ 1.58 lb/in2 Use a calculator. Answer: The atmospheric pressure at an altitude of about 10 miles will be approximately 1.6 lb/in2.

Assignment Pg. 455 #2-4 all (Graph) #7 #12 #34