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Name:__________ warm-up 7-1 Solve 4a2 – 9 = 0 Solve 6y3 + 13y2 + 5y = 0 Find (f + g)(x) if f(x) = 3x + 7 and g(x) = x2 – 10. Determine whether f(x) = 4x – 9 and g(x) = are inverse functions.

Details of the Day Activities: Graph exponential growth functions. EQ:How do exponential functions model real world problems and their solutions? I will be able to… Activities: Warm-up Review homework Notes: Review for test Class work/ HW Vocabulary: *exponential function exponential growth asymptote growth factor exponential decay decay factor Graph exponential growth functions. . . Graph exponential decay functions.

7-1 Exponential functions Slope

A Quick Review Solve 4a2 – 9 = 0 Solve 6y3 + 13y2 + 5y = 0 Find (f + g)(x) if f(x) = 3x + 7 and g(x) = x2 – 10. Determine whether f(x) = 4x – 9 and g(x) = are inverse functions.

A Quick Review

Notes and examples Graph y = 4x. State the domain and range. x y

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Notes and examples

Notes and examples Graph the function y = 3x – 2. State the domain and range Domain: Range: x y

Notes and examples Graph the function y = 2x – 1. State the domain and range. Domain: Range: x y

Notes and examples Graph the function y = 2x – 4 Domain: Range: x y

Notes and examples Graph the function y = 4x – 2 + 3 Domain: Range: x

Notes and examples 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 x y

Notes and examples 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? x y

Notes and examples Graph the function x y

Notes and examples Graph the function x y

Notes and examples 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 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. x y

Notes and examples B. AIR PRESSURE The pressure of a car tire with a bent rim is 34.7 lb/in2 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. x y

Notes and examples

Notes and examples