Exponential Function Word Problems

Solve real-world problems with exponential functions! Practice identifying growth and decay rates.

Review from before break Watch the video below to review the parts of an exponential equation and exponential growth SECTION 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 3 2 1.2 0.25 .5 1.50 3 .95 NOTES EXAMPLE 1 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 NOTES EXAMPLE 2 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! SECTION 2: Fill in the blank Ms. Abundis is opening a bank account for the summer. The amount of money she has each week can be represented with the exponential functiony = 5(1.2)x , where x represents the number of weeks. Fill in the blanks below:Ms. Abundis starts with 5 dollars, which is the a-value in the equation. The money in her account is exponentially increasing, since 1.2 is the b-value and is greater than 1. Ms. Flores is addicted to online shopping. The amount of money she has each week can be represented with the exponential function y = 200(0.85)x , where x represents the number of weeks. Fill in the blanks below: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. The population of birds in Ms. Perez's neighborhood is expected to decline each year and is modeled by the equation y = 200,000(0.5)x , where x represents the number of years. Fill in the blanks: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. 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. Fill in the blanks: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. SECTION 3: Multiple ChoiceThe 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). The 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. The population of Boringtown decreased annually by 1.8% between the year 2015-2018. In 2015, there were approximately 200,000 people living in Boringtown. Which function models the city's population since 2015? y = 200,000(1 + 0.018)3 y = 200,000(1 - 0.18)3 y = 200,000(1 + 0.18)3 y = 200,000(1 - 0.018)3 The original value of a painting is $1400, and the value increases by 9% each year. Write an exponential growth function to model this situation. y=1400(1.09)x y=1.09(1400)x y=1400(0.91)x y=1.09x Most automobiles depreciate as they get older. Suppose an automobile that originally costs $14,000 depreciates by 20% of its value every year. What exponential equation can we create to model this situation? y=14000(.20)x y=14000(.80)x y=14000(1+.20)x y=14000(1+.80)x What is the percent (%) of increase or decrease in the following function?f(x) = 3000 (1 + 0.4)x Decrease by 4% Increase by 4% Increase by 40% Decrease by 40% Identify the percent (%) increase or decrease for the function below:f(x) = 3000 (1.17)x Increase by 0.17% Increase by 17% Decrease by 17% Decrease by 0.17%