Graph y = 2 1 3 𝑥 −1 – 2. Asymptote: _______ Domain: _________ Range: ___________ Problem of the Day

Section 7-1b Graphing Exponential Functions

Then Now Objectives You graphed exponential growth and decay function. Solve exponential growth equations. Solve exponential decay equations.

Common Core State Standards Content Standards F.IF.7.e – Graph exponential and logarithmic functions, showing intercepts and end behavior. F.IF.8.b – Use the properties of exponents to interpret expressions for exponential functions. Mathematical Practices 3) Construct viable arguments and critique the reasoning of others. Common Core State Standards

Exponential Growth 𝐴 𝑡 =𝑎(1+𝑟 ) 𝑡 The function can be used to find the amount A(t) after t time periods, where a is the initial amount and r is the percent of increase per time period. Note that the base of the exponential expression, 1 + r, is called the growth factor.

The first U. S. census was conducted in 1790 The first U.S. census was conducted in 1790. At that time, the population was 3,929,214. Since then, the U.S. population has grown by approximately 2.03% annually. Based off of this information, what should the population be today? Example 3

Teen spending is expected to grow 3. 5% annually from $79 Teen spending is expected to grow 3.5% annually from $79.7 billion in 2016. When will teen spending reach $150 billion? Example 3

In 2000, there were 738,000,000 people worldwide using the Internet In 2000, there were 738,000,000 people worldwide using the Internet. At that time, the number of users was growing by 11.5% annually. How many people will be using the internet in 2025? Example 3

Exponential Decay 𝐴 𝑡 =𝑎(1−𝑟 ) 𝑡 The function can be used to find the amount A(t) after t time periods, where a is the initial amount and r is the percent of decrease per time period. Note that the base of the exponential expression, 1 – r, is called the decay factor.

A cup of black tea contains about 68 milligrams of caffeine A cup of black tea contains about 68 milligrams of caffeine. The average teen can eliminate approximately 12.5% of the caffeine from their system per hour. Estimate the amount of caffeine in the body 2 hours after drinking a cup of black tea. Example 5

The pressure of the atmosphere is 14. 7 lb/ 𝑖𝑛 2 at Earth’s surface 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. Example 5

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