Exponential Functions and Growth Scenarios in Mathematics
Explore exponential functions through real-life scenarios such as bacterial growth and zombie virus infection, solve practice problems on linear and exponential functions, and delve into drug filtering calculations. Learn to write explicit rules for exponential functions and calculate percent increase or decrease from exponential equations.
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Exponential Functions 1/30/2013
Warm-Up 3: 2.5.2014 1. A population of 25 bacteria doubles in size every week. a) Write an exponential function to model this. b) What will the population be in 7 weeks? 2. Suppose a Zombie virus has infected 40 people at our school. The number of zombies doubles every hour. a) Write an equation that models this. b) How many zombies are there after 1 day?
HW 5.6 Check 1a) Linear 1c)linear 2. A) 9, 11, 13, 15, 17, 19 B) 81, 243, 729, 2187, 6561, 19683 c) 8, 9.50. 11, 12.50, 14, 15.50 d) 16, 32, 64, 128, 256, 512 3a) $100 3b) $29524 3c) $87.5 3D) $1023 1b)exponential 1d)exponential
Essential Question (2.5.2014) How do I write explicit rules for exponential functions?
Growth Factor to Percent Find the percent increase or decease from the following exponential equations. Remember either b=1+r or b=1-r 1. Y = 3(.5)x 2. Y = 2(2.3)x 3. Y = 0.5(1.25)x
Ex 1. Suppose the depreciation of a car is 15% each year? A) Write a function to model the cost of a $25,000 car x years from now. B) How much is the car worth in 5 years?
Ex 2: Your parents increase your allowance by 20% each year. Suppose your current allowance is $40. A) Write a function to model the cost of your allowance x years from now. B) How much is your allowance the worth in 3 years?
Complete the 2 practice problems On your Drug Filtering worksheet from yesterday.
Other Drug Filtering Problems 1. Assume that your kidneys can filter out 10% of a drug in your blood every 6 hours. You take one 200-milligram dose of the drug. Fill in the table showing the amount of the drug in your blood as a function of time. The first two data points are already completed. Round each value to the nearest milligram.
TIME SINCE TAKING THE DRUG (HR) AMOUNT OF DRUG IN YOUR BLOOD (MG) 0 6 12 18 24 30 36 42 48 54 60 66 200 180
A) How many milligrams of the drug are in your blood after 2 days? B) A blood test is able to detect the presence of the drug if there is at least 0.1 mg in your blood. How many days will it take before the test will come back negative? Explain your answer.
2. Calculate the amount of drug remaining in the blood in the original lesson, but instead of taking just one dose of the drug, now take a new dose of 1000 mg every four hours. Assume the kidneys can still filter out 25% of the drug in your blood every four hours. Have students make a complete a table and graph of this situation.
TIME SINCE TAKING THE DRUG (HR) 0 4 8 12 16 20 24 28 32 36 40 44 48 AMOUNT OF DRUG IN YOUR BLOOD (MG) 1000 1750 2312
A) How do the results differ from the situation explored during the main lesson? Refer to the data table and graph to justify your response. B) How many milligrams of the drug are in your blood after 2 days?
