Warm-Up Identify each variable as the dependent variable or the independent for each of the following pairs of items the circumference of a circle the measure of the radius the price of a single compact disc the total price of three compact discs time spent studying for a test score on the test number of hours it takes to type a paper the length of the paper amount of your monthly loan payment the number of years you need to pay back the loan number of tickets sold for a benefit play the amount of money made

HW Check In two years there were 40 lizards After one year there were 20 lizards 4 years a1 = 10

5.6 Exponential Decay Unit 5 Day 6

5.6 Drug Filtering Assume that your kidneys can filter out 25% of a drug in your blood every 4 hours. You take one 1000-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 three data points are already completed. Round each value to the nearest milligram

Time since taking the drug (hrs) Amount of drug in your blood (mg) 1000 4 750 8 562.5 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68

How many milligrams of the drug are in your blood after 2 days? Will you ever completely remove the drug from your system? Explain your reasoning. 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.

Recall: y = a•bx Initial (starting) value = a Growth or Decay Factor = b x is the variable, so we change that value based on what we are looking for! Remember that the growth or decay factor is related to how the quantities are changing. Growth: Doubling = 2, Tripling = 3. Decay: Taking half = Taking a third =

Growth : b is greater than 1 Decay: When b is between 0 and 1! Exponential Decay Growth : b is greater than 1 Decay: When b is between 0 and 1!

When the rate of increase or decrease is a percent: we use this notation for b: 1 + r for growth 1 – r for decay (r is the rate written as a decimal)

Complete Ex 1 and Ex 2 on the bottom of this page.

Ex 1. Suppose the depreciation of a car is 15% each year? Write a function to model the cost of a $25,000 car x years from now. 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. Write a function to model the cost of your allowance x years from now. How much is your allowance the worth in 3 years?

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) 200 6 180 12 18 24 30 36 42 48 54 60 66

How many milligrams of the drug are in your blood after 2 days? 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) AMOUNT OF DRUG IN YOUR BLOOD (MG) 1000 4 1750 8 2312 12 16 20 24 28 32 36 40 44 48

How do the results differ from the situation explored during the main lesson? Refer to the data table and graph to justify your response. How many milligrams of the drug are in your blood after 2 days?

HW 5.6