After a dog or cat is given a preventive flea medicine, the medicine begins to break down in the animal’s bloodstream. With each passing hour, there is less active medicine in the blood.
a. Complete the table and then draw a graph to show the amount of active medicine in a dog or cat’s bloodstream each hour for 6 hours after a 20-milligram dose.
This is what is given in the table:
Time since dose (hours) Active medicine in blood (milligrams)
0 20
1 10
This is how I completed the table:
Time since dose (hours) Active medicine in blood (milligrams)
0 20
1 10
2 5
3 2.5
4 1.25
5 0.625
6 0.3125
b. Write an equation to model the relationship between the number of hours since the dose was administered, h, and the miligrams of active medicine, m.
Since my graph shows this is exponential decay, since it's losing medicine each hour, I wrote my equation as:
m = 20(.5)^h
c. c. How much active medicine would be in the animal’s bloodstream after 10 hours?
0.0195 mg
Thank you for checking my answers for me.
Your answers are correct : )
a. Your completion of the table and the values you have provided are correct. The active medicine in the bloodstream decreases by half with each passing hour.
b. Your equation to model the relationship between the number of hours since the dose was administered, h, and the milligrams of active medicine, m, is also correct. The equation you have written, m = 20(.5)^h, represents exponential decay, where the initial amount of medicine is 20 milligrams, and each hour it is reduced by half.
c. To find out how much active medicine would be in the animal's bloodstream after 10 hours, you can substitute the value of h = 10 into the equation: m = 20(.5)^10. Evaluating this expression gives us a result of approximately 0.0195 mg.
Your answers are correct. Well done!