Veterinarians use different medications to treat dogs for fleas. Once administered, the medication typically decays exponentially. One treatment decays by half each week.

A dog receives 4 mL of medication and the function f gives the number of mL of medicine left after w weeks.

f(x) = 4 (1/2)^w

Reply as ansers 1a, 1b, 1c, 2.

Find the amount of medication in the dog’s bloodstream 1 week, 2 weeks, and 3 weeks after it is administered.

a.) 1 week b.) 2 weeks c) 3 weeks.

Explain what F(4/7)

means in this context. The 7 means the number of days in 1 week.

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warylucknow warylucknow · Answer 1 · 2020-05-21T09:23:19+02:00

Answer:

(a) The amount of medication in the dog’s bloodstream 1 week is 2 ml.

(b) The amount of medication in the dog’s bloodstream 2 weeks is 1 ml.

(c) The amount of medication in the dog’s bloodstream 3 weeks is 0.50 ml.

Step-by-step explanation:

The decay function is:

[tex]y=a(1-r)^{t}[/tex]

Here,

y = final amount

a = initial amount

r = decay rate

t = time

The function representing the number of ml of medicine left after w weeks, when a dog receives 4 ml of medication is:

[tex]f(x)=4\cdot (\frac{1}{2})^{w}[/tex]

(a)

Compute the amount of medication in the dog’s bloodstream 1 week as follows:

[tex]f(x)=4\cdot (\frac{1}{2})^{w}\\\\f(1)=4\cdot (\frac{1}{2})^{1}\\\\=4\times\frac{1}{2}\\\\=2\ \text{ml}[/tex]

Thus, the amount of medication in the dog’s bloodstream 1 week is 2 ml.

(b)

Compute the amount of medication in the dog’s bloodstream 2 weeks as follows:

[tex]f(x)=4\cdot (\frac{1}{2})^{w}\\\\f(2)=4\cdot (\frac{1}{2})^{2}\\\\=4\times\frac{1}{4}\\\\=1\ \text{ml}[/tex]

Thus, the amount of medication in the dog’s bloodstream 2 weeks is 1 ml.

(c)

Compute the amount of medication in the dog’s bloodstream 3 weeks as follows:

[tex]f(x)=4\cdot (\frac{1}{2})^{w}\\\\f(3)=4\cdot (\frac{1}{2})^{3}\\\\=4\times\frac{1}{8}\\\\=0.50\ \text{ml}[/tex]

Thus, the amount of medication in the dog’s bloodstream 3 weeks is 0.50 ml.