Do Now: - Evaluate round to the nearest hundredth Exponential Functions, Growth and Decay Understand how to write and evaluate exponential expressions to model growth and decay situations. Do Now: - Evaluate round to the nearest hundredth 1. 100(1.08)20 2. 100(0.95)25 3. 100(1 – 0.02)10 ≈ 466.1 GET a Calculator!! ≈ 27.74 ≈ 81.71 Today’s Agenda Success Criteria: Do Now Hand Back Test Activity I can graph an exponential function Identify exponential growth and decay

Intro exponentials Act 1 Algebra I Production

What Questions do YOU have? Math Rules! Act 1 What Questions do YOU have?

66 mm 156 mm Think Tank Pair Share Act 2 2nd, 3rd, 9th copy?

Act 3

On the back of your paper answer the following: What are the dimensions of the 100th copy? Generalize; what is the nth copy? Would it ever disappear? Justify

Sequel What are the values that we need? Algebra I Strikes Back What are the values that we need? How much money is in Fry’s bank account?

Summarize The End

Entry Task: Zombies Present in Local High Schools Exponential Functions, Growth and Decay Understand how to write and evaluate exponential expressions to model growth and decay situations. Entry Task: Zombies Present in Local High Schools 2/28/18 BREAKING NEWS: The Todd Beamer Titans have been quarantined in their school to decrease the chance of Solanum spreading to the rest of Federal Way. Students in math classes may be at a higher risk, since the virus has been extremely active. Zombies must infect one other person per day in order to stay alive. It is expected that the virus will spread next to neighboring towns and cities. Mr. Lee, Mr. Wang, and Mr. Kutschara all teach one algebra I class. Today, they each have 1 infected person in their Alg I class. Assuming all of the zombies stay alive, how long will it take until there are 1,018 infected students at Todd Beamer? Today’s Agenda Success Criteria: Do Now Lesson HW #12 I can graph an exponential function Identify exponential growth and decay

Growth that doubles every year can be modeled by using a function with a variable as an exponent. This function is known as an exponential function. The parent exponential function is f(x) = bx, where the base b is a constant and the exponent x is the independent variable.   The y-intercept is (0,a), the domain is all real numbers, the asymptote is y = 0 and the range is y > 0.

The graph of the parent function f(x) = 2x is shown The graph of the parent function f(x) = 2x is shown. The domain is all real numbers and the range is {y|y > 0}.

Notice as the x-values decrease, the graph of the function gets closer and closer to the x-axis. The function never reaches the x-axis because the value of 2x cannot be zero. In this case, the x-axis is an asymptote. An asymptote is a line that a graphed function approaches as the value of x gets very large or very small.

A function of the form f(x) = abx, with a > 0 and b > 1, is an exponential growth function, which increases as x increases. When 0 < b < 1, the function is called an exponential decay function, which decreases as x increases. In the function y = bx, y is a function of x because the value of y depends on the value of x. Remember! Negative exponents indicate a reciprocal. For example: Remember!

Example 1A: Exponential Functions Tell whether the function shows growth or decay. Then find the y-intercept. Find the value of the base. The base , ,is less than 1. This is an exponential decay function.

Check It Out! Example 1 Tell whether the function p(x) = 5(1.2x) shows growth or decay. Then find the y intercept. Find the value of the base. p(x) = 5(1.2 x) The base , 1.2, is greater than 1. This is an exponential growth function.

Example 1B: Graphing Exponential Functions Without graphing determine whether the function represents exponential growth or decay. Then find the y intercept. g(x) = 3(2)x Find the value of the base. g(x) = 3(2)x The base, 2, is greater than 1. This is an exponential growth function. g(x) = 3(2)x The y intercept is (0,a). The y intercept is at 3 Step 2 Graph the function by using a graphing calculator.

Amount after t time periods You can model growth or decay by a constant percent increase or decrease with the following formula: Amount after t time periods Number of time periods   Initial Amount   In the formula, the base of the exponential expression, 1 + r, is called the growth factor. Similarly, 1 – r is the decay factor.

Lesson YOU TRY In 2000, the world population was 6.08 billion and was increasing at a rate 1.21% each year. 1. Write a function for world population. Does the function represent growth or decay? P(t) = 6.08(1.0121)t 2. Use a calculator to predict the population in 2020. ≈ 7.73 billion The value of a $3000 computer decreases about 30% each year. 3. Write a function for the computer’s value. Does the function represent growth or decay? V(t)≈ 3000(0.7)t 4. Use a calculator to predict the value in 4 years. ≈ $720.30 Gabby purchased a car for $5000. A year later the car was valued at $4500. 5. Write a function that represents the value of the car. C(t)≈ 5000(1-0.1)t 6. At this rate of depreciation, how many years until her car is worth $1000? ≈ ?? years

HW#12