Question

PLS HELP!!! Lesson 3: Understanding Rational Inputs Cool Down: Flea Treatment Veterinarians use different medications to treat fleas in dogs. Once administered, the medication typically decays exponentially. One treatment decays by half each week. A dog receives & mL of medication and the function f gives the number of mL of medicine left after w weeks. 1. Find the amount of medication in the dog's bloodstream 1 week, 2 weeks, and 3 weeks after it is administered. 2. Write an expression to represent the amount of medication in its bloodstream 1 day after it is administered. 3. Explain what f (2) means in this context.​

Answer 1

1. We are told that the medication decays by half each week. So, after one week, the amount of medication remaining is half of the original dose:

f(1) = (1/2) × &mL; = ½ &mL;

After two weeks, the amount of medication remaining is half of what was left after one week:

f(2) = (1/2) × ½ &mL; = ¼ &mL;

After three weeks, the amount of medication remaining is half of what was left after two weeks:

f(3) = (1/2) × ¼ &mL; = ⅛ &mL;

2. We are told that the medication decays by half each week. To find the amount of medication remaining one day after it is administered, we need to find the amount of medication that decays in one day. There are 7 days in a week, so the medication decays by a factor of ½ each &frac17; of a week. Therefore, the amount of medication remaining after one day is:

f(1/7) = ½ × &mL; = ½ &mL;

3. f(2) represents the amount of medication remaining in the dog's bloodstream two weeks after it is administered. We can plug w = 2 into the function f to find this amount, which is ¼ &mL.