Question

A doctor prescribes a pill for Tammy’s headache. The pill has 500 milligrams. This type of medication decays at a rate of 10% per hour.

a. Write an equation representing the amount of medication left in Tammy’s body after n hours.
b. How much medicine is left in Tammy’s body after 3 hours? 24 hours?
c. Create a graph to represent the medication in Tammy’s body over time.
d. Use your graph to estimate the half-life of this medication.
e. What is the range of this situation? What does this tell you about how long it takes for the medicine to completely leave the body?

Answer 1

a) M(n)=500−0.10n

b) 499.7, and 497.6 milligrams

c) The table and graph are below

d) 2500 hours

e) Range [0,500] milligrams

Domain [0,5000] hours

Other answers are below

Explanation:

a) The equation representing the amount of medication, M, left in Tammy's body after n hours

M(n)=500−0.10n

b) When n=3 hours we have

M(3)=500−0.10(3)=499.7 mg

When n=24 hours we obtain

M(24)=500−0.10(24)=497.6 mg

c) Table

n,Times (hours)

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

​M(n),Medication (mg)

500

450

400

350

300

250

200

150

100

50

0

The graph is in picture

d. Use your graph to estimate the half-life of this drug.

According to the table and the graph, the half-life is 2500 hours.

M(2500)=500−0.10(5000)=250 milligrams

e. What is the range of this situation?

From the time it is ingested until it is completely assimilated, 500 hours elapse

Range [0,500] mg

What does this tell you about the time it takes for the drug to completely leave the body?

500 hours divided by the 24 hours of the day is approximately

550/24 = 208.33 days or approximately 2008.33/30 = 7 month

The table and graph are in the pictures

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