College

We appreciate your visit to Answer the following questions Show all the work necessary to solve the problem Write neatly and clearly mark your answer 1 A medicine has a. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

Answer the following questions. Show all the work necessary to solve the problem. Write neatly and clearly mark your answer.

1. A medicine has a half-life of 8 hours. If you take an initial dose of 2000 milligrams:

a. How much medicine will remain in your body after 20 hours?

b. How much medicine will remain in your body after 2 days?

2. The number of people infected with a virus doubles every three days. If you start with 100 infected people:

a. How many people will be infected after 9 days?

b. How many people will be infected after 15 days?

Answer :

Below is a detailed, step-by-step solution.

________________________________

1. A medicine has a half-life of 8 hours. If the initial dose is [tex]$2000$[/tex] milligrams, the amount remaining in the body after [tex]$t$[/tex] hours is given by

[tex]$$
A(t) = 2000 \left(\frac{1}{2}\right)^{t/8}.
$$[/tex]

(a) To find the amount remaining after [tex]$20$[/tex] hours, substitute [tex]$t = 20$[/tex]:

[tex]$$
A(20) = 2000 \left(\frac{1}{2}\right)^{20/8} = 2000 \left(\frac{1}{2}\right)^{2.5}.
$$[/tex]

Evaluating [tex]$\left(\frac{1}{2}\right)^{2.5}$[/tex] gives approximately [tex]$0.17678$[/tex], so

[tex]$$
A(20) \approx 2000 \times 0.17678 \approx 353.55 \text{ milligrams}.
$$[/tex]

(b) For [tex]$2$[/tex] days, note that [tex]$2$[/tex] days equal [tex]$48$[/tex] hours. Substitute [tex]$t = 48$[/tex]:

[tex]$$
A(48) = 2000 \left(\frac{1}{2}\right)^{48/8} = 2000 \left(\frac{1}{2}\right)^{6}.
$$[/tex]

Since [tex]$\left(\frac{1}{2}\right)^6 = 0.015625$[/tex], we have

[tex]$$
A(48) \approx 2000 \times 0.015625 = 31.25 \text{ milligrams}.
$$[/tex]

________________________________

2. The number of people infected with a virus doubles every three days. If the initial number of infected people is [tex]$100$[/tex], the number after [tex]$t$[/tex] days is given by

[tex]$$
P(t) = 100 \cdot 2^{t/3}.
$$[/tex]

(a) After [tex]$9$[/tex] days, substitute [tex]$t = 9$[/tex]:

[tex]$$
P(9) = 100 \cdot 2^{9/3} = 100 \cdot 2^{3}.
$$[/tex]

Since [tex]$2^3 = 8$[/tex], it follows that

[tex]$$
P(9) = 100 \cdot 8 = 800 \text{ people}.
$$[/tex]

(b) After [tex]$15$[/tex] days, substitute [tex]$t = 15$[/tex]:

[tex]$$
P(15) = 100 \cdot 2^{15/3} = 100 \cdot 2^{5}.
$$[/tex]

Since [tex]$2^5 = 32$[/tex], then

[tex]$$
P(15) = 100 \cdot 32 = 3200 \text{ people}.
$$[/tex]

________________________________

In summary:

1. (a) After 20 hours, approximately [tex]$353.55$[/tex] milligrams remain.
  (b) After 2 days (48 hours), approximately [tex]$31.25$[/tex] milligrams remain.

2. (a) After 9 days, there will be [tex]$800$[/tex] infected people.
  (b) After 15 days, there will be [tex]$3200$[/tex] infected people.

Thanks for taking the time to read Answer the following questions Show all the work necessary to solve the problem Write neatly and clearly mark your answer 1 A medicine has a. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada