SWBAT: Graph exponential functions and find exponential curves of best fit

Transcription

1 Algebra II: Exponential Functions Objective: We will analyze exponential functions and their properties SWBAT: Graph exponential functions and find exponential curves of best fit Warm-Up 1) Solve the following absolute value inequalities 3xx < xx + 4 > 9 2) y varies jointly with the square of x and the square root of t. If k is the constant of proportionality, write an equation for y. 3) 4)

2 Exponential Functions Case-1) A sleeper cell of zombies executed an evil plan 10 years in the making. Their objective: to "turn" the entire human race into evil zombies! Each zombie can turn 2 humans per day, but they are not sure how long it will take them to completely turn every human on the planet. Complete the table below to show how many total zombies there will be every day for the first 5 days of the attack. The original sleeper cell had only 5 members, but keep in mind that newly turned zombies also have the power (and the will!) to turn other humans. Graph your results. Day (x) Zombies (y) x Case-2) The zombies decide they need to up their game. They now plan to turn 3 humans per day. Complete the table below to show how many zombies will there be after 5 days. Plot your results on the graph above. Day (x) x Zombies (y) = = = = (4) x Can you develop an equation that relates the number of infected people versus days? Case-1 (turn 2 humans per day) y = Case-2: (turn 3 humans per day) y =

3 These equations are known as Exponential Functions. They take the form y = a x, where a > 0 (but not equal to 1) Note the difference between Exponential Functions and other functions we have studied some examples Quadratic: yy = xx 2 Radical: yy = xx 1/2 Exponential: yy = (2) xx Case-3: There is a radiation spill at a plant. The radiation level at the start (x = 0) is 100. Each year thereafter, the radiation level is cut in half. Use the table below to find the radiation level each year for the first 5 years. Graph your results. Year (x) Radiation (y) x What is the equation that relates radiation level (y) to years (x)? y =

4 Exponential Growth Exponential Decay yy = 3 xx yy = xx >1 <1 Exponential Curves of Best-Fit and Analysis Example-1: A cup of soup is left to cool. The table below gives the temperature in degrees Fahrenheit, of the soup recorded over a 10-minute period. Time in Minutes (x) Temperature in (y) Exponential Regression to find the curve of best fit: Use Stat Edit to enter the data into lists Use Stat Calc 0:ExpReg to find values (NOTE: Scroll down to find 0 below 9) a) Write an exponential curve of best fit rounding all values to the nearest thousandth. b) Estimate the temperature of the soup in 20 minutes.

5 You Try 1) The table below shows the number of stores in a store chain. x = 1 represents the year The number of stores grow exponentially. Estimate the number of stores in the year 2020 (x = 12). Year Stores Year Stores ) $46,200 dollars is invested in a company. Over the next 5 years, the value of the investment decays exponentially as shown in the table below. Estimate the value of the investment in 10 years. Year Stores 0 46, , , , , ,000

6 Real Exponential Equation Solving Problem 1) Graphically solve for x in the following exponential equations: 1 = 5(0.3) xx 4 = 2(1.1) xx 2) Challenge Question: The radiation level (y) at the Chernobyl nuclear disaster site as a function of years (x) is estimated to by the exponential decay equation yy = 100(0.995) xx The radiation level safe for humans is 1. How many years will it be safe for humans to live at Chernobyl? Do this graphically and prepare to zoom out a lot (zoom out 4 or 5 times).