Transcript 5.6 Exponential Decay

Warm-Up
Identify each variable as the dependent variable or the
independent for each of the following pairs of items
1. the circumference of a circle
the measure of the radius
2. the price of a single compact disc
the total price of three compact discs
3. time spent studying for a test
score on the test
4. number of hours it takes to type a paper
the length of the paper
5. amount of your monthly loan payment
the number of years you need to pay back the loan
6. number of tickets sold for a benefit play
the amount of money made
HW Check
1. In two years there were 40 lizards
2. After one year there were 20 lizards
3. 4 years
4.
5. a1 = 10
6.
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)
0
4
8
12
16
20
24
28
32
36
40
44
48
52
56
60
64
68
1000
750
562.5
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.
Recall:
y=
x
a•b
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 =
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?
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?
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
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?
HW 5.6