1/20/21 M1 EXPONENTIAL FUNCTIONS REVIEW

Choose the correct term to complete each sentence. The type of function y=a(b)ˣ models Exponential Decay for when b is in between 0 and 1.The function y=a(b)ˣ models Exponential Growth for when b is greater than 1.The type of function y=a(b)ˣ represents is Exponential Function Reminders for when you are looking at exponential graphs visually... Exponential GROWTH increasesas you read the graph from left to right.Exponential DECAY decreasesas you read the graph from left to right. Which graph(s) represent exponential growth? (Select all that apply). Which graph(s) represent exponential growth? (Select all that apply). Which graph(s) represent exponential decay? (Select all that apply). Does this graph represent exponential growth, decay, or neither? Growth Decay Neither Given the following functions, identify the rate, rate factor, rate percent, and initial value. Also identify which function is a growth and which one is a decay. Rate 0.97 0.65 Rate Percent 97% 65% Initial Value 400 27 Growth f(x) = 27(1.65)ˣ Decay g(x) = 400(0.03)ˣ Identify the common ratio Given the table below, identify the growth or decay factor (b) of the exponential function. Match each variable from y = a(b)x to its meaning. a starting amount b growth factor x time y total result Sort growth and decay factors into the correct groups. Growth 1.01 2 1.2 10 1.85 7 9 Decay 0.4 0.999 1 3 0.75 Which equation below represents a bank account with $400 earning 2% interest per year? y = 400(1.2)x y = 400(1.02)x y = 400(0.8)x y = 400(2)x Which equation below represents a car valued at $8500 losing 9% of its value each year? y = 8500(0.1)x y = 8500(1.09)x y = 8500(1.9)x y = 8500(0.91)x The equation y = 2600(1.01)x represents the number of students in a school district whose population is increasing 1% per year. How many students can the district expect to have in 11 more years? Round appropriately. 2900 Students 2901 Students The equation y = 30,000(0.999)x represents the population of a city that is losing .1% of its population each month. What will the population be after 2 years? 29,940 people 29,288 people 29,642 people Which equation below shows a starting amount of 15 and a growth factor of 3? y = 15(3)x y = 3(15)x y = 15(x)3 y = 3(x)15 What percent decrease is represented by the decay factor 0.72? 28% 72% 0.72% Initial Value and Percent of Increase For each question identify the initial value (I.V.) and the percent of increase. DO NOT USE THE PERCENT SIGN (%). Equation Initial Value (I.V.) Percent of Increase y = -5(3.4)x -5 240 y = 5.8(2.101)x 5.8 110.1 y = (1.121)x 1 12.1 y = 8(1.335)x 8 33.5 Matching: Exponential Decay Match the following exponential equations with its appropriate situation. Each equation will match with exactly one situation. Remember, when calculating the decay rate, it is 1 - r. So if the decay rate is 40%, then 1 - 0.4 = 0.6. y =14000(0.98)^x The populations of a town in the year 2000 was 14,000. It is losing people at a rate of 2% per year. y = 14000(0.8)^x Your parents bought a car for $14,000. Each year they have the car, it loses 20% of its value. y = 14000(0.2)^x Your x-box has 14,000 kilobits of storage. Each year you have it, it loses 80% of its storage from the games you play. y = 14000(0.92)^x You bought a jumbo bag of candy for quarantine. It has 14,000 pieces originally. You eat the candy at a rate of 8% per day. y = 14000(0.95)^x There are 14,000 photos saved to your camera roll! You plan to delete them all at a rate of 5% each day.