Exponential Decay 2/5/2013

Warm-Up 3 (2.4.2014)1. Create a geometric sequence with 4

terms.

2. Write an explicit rule for the table:

3. How many bacteria would there be at hour 6?

Hours Number of

bacteria0 41 162 643 256

1. In year 2 there are 40 lizards2. In year 1 there are 20 lizards3. At about 3.5 years4. and this continues

5. 10

6. Keep multiplying by 2 each year.

Homework Check 5.5

HW 5.10 Check

1. y=302.89 2. quarterly, $0.32 more

3. 402.55 4. 3486784401

5. a) b) c)

Drug FilteringAssume 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)

0 10004 7508 562

121620242832364044485256606468

3. How many milligrams of the drug are in your blood after 2 days?

4. Will you ever completely remove the drug from your system? Explain your reasoning.

5. 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.

Initial (starting) value = aGrowth or Decay Factor = bx 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: Losing half = Losing a third =

Recall: y = a•bx

Exponential Decay Is When b is between 0 and

1!

Growth : b is greater than 1

If the rate of increase or decrease is a percent:

we use a base of 1 + r for growth

or 1 – r for decay

r = rate as a DECMIAL!

Finding our Base! What would b be in our equation?

Either b=1+r or b=1-r1. Increase of 25% 2. increase of 130%

3. Decrease of 30% 4. Decrease of 80%

Growth Factor to PercentFind 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

Other Drug Filtering Problems1. 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 TAKINGTHE DRUG (HR)

AMOUNT OF DRUGIN YOUR BLOOD (MG)

0 2006 18012182430364248546066

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 TAKINGTHE DRUG (HR)

AMOUNT OF DRUGIN YOUR BLOOD (MG)

0 10004 17508 231212162024283236404448

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?

HW 5.6

HW 5.10