Week 8: May 11 Exponential Functions in the REAL WORLD

Master exponential functions with real-world examples! Understand growth, decay, and more.

Week 8 Objectives RecallIn an exponential equation y = a(b)x, the 'a' stands for the initial amount (also the y-intercept) and the 'b' stands for the growth or decay rate. Growth or Decay Rate Watch the video below to review the parts of an exponential equation and exponential growth from last week. 1. Exponential Equations Parts Identify the different parts of an exponential equation and fill in the table by clicking the yellow squares. Equation: 'a' value 'b' value Growth or Decay? 3 2 Growth (increasing) 1.2 0.25 Decay (decreasing) .5 1.50 Growth (increasing) 3 .95 Decay (decreasing) Interpreting an Exponential Equation with the Bee Population Watch this short video over how to interpret an equation from a word problem (which you will do below).If you want more information on bees, visit Interpreting an Exponential Equation with Humans in the World Watch this short video to learn about how to interpret an equation about the number of people in the world! There will be questions below over this topic.You can learn more about the world population here when you finish your assignment! For questions 2 and 3, read each part and fill in the blanks below the questions. 2. ALL ABOUT THE MONEYPart A:Ms. Abundis is opening a bank account for the summer. The amount of money she has each week can be represented with the exponential function below:y = 5(1.2)x, where x represents the number of weeks.Part B:Ms. Flores is addicted to online shopping. The amount of money she has each week can be represented with the exponential function below:y = 200(0.85)x , where x represents the number of weeks. Answer A:Ms. Abundis starts with 5 dollars, which is the a-value in the equation. The money in her account is exponentiallyincreasing, since 1.2 is the b-value and is greater than 1.Answer B:Ms. Flores starts with 200 dollars, which is the a-value in the equation. The money in her account is exponentially decreasing, since 0.85 is the b-value and it is less than 1. 3. POPULATIONSPart A:The cat population in Coach Cruz's neighborhood during the summer can be modeled by the equation below,y = 250(4)x, where x represents the number of weeks.Part B:The population of birds in Ms. Perez's neighborhood is expected to decline each year and is modeled by the equationy = 200,000(0.5)x , where x represents the number of years. Answer A:The 'a' value of the equation is 250, which represents the initial number of cats in Coach Cruz's neighborhood. The 'b' value is 4, which represents the growth rate. The cat population shows exponential growth.Answer B:The 'a' value of the equation is 200,000, which represents the initial number of birds in Ms. Perez's neighborhood. The 'b' value is 0.5, which represents that the population of birds is exponentially decaying. 4. BACTERIAThe number of bacteria on your hands when they are dirty can be determined by the equation y = 2(1.05)x, where x is the number of seconds.What does the "a" value represent? We started with 1.05 bacteria on our hands. We started with 2 bacteria on our hands. The bacteria was exponentially growing (increasing). The bacteria was exponentially decaying (decreasing). 5. VIRUSThe flu was brought to Lanier by someone who was sick. The number of people being infected with the virus can be represented by the equation y = 1(2)x, where x represents each hour that goes by since the flu arrived.What does the 2 represent in the equation? The virus began with 2 people. The virus is exponentially decreasing by a factor of 2 The virus is exponentially increasing by a factor of 2. The flu began with 2 viruses. Creating Exponential Graphs Please draw an exponential function which represents :* GROWTH* Y-intercept of 3 in the graph below.* Asymptote of y=1 ***Extra Credit*** If 4 people brought the flu to Lanier, and each one talked to 3 people every hour, what do you think the equation would be? Explain your reasoning