Question

At 5:00 p.m., Vera took 400 milligrams

of medicine to help relieve her headache.
The table below shows the amount of
medicine in her system at different
hours. If this pattern continues, find
the approximate amount of medicine in
her system when she wakes up at
7:00 a.m. the next morning. Round to the nearest tenth.
5:00pm - 400mg
6:00pm - 350mg
7:00pm - 306.25mg

Answer 1

To find the approximate amount of medicine in Vera's system when she wakes up at 7:00 a.m., observe the pattern of the amount of medicine at different hours and multiply by 0.875 each hour.

Step-by-step explanation:

To find the approximate amount of medicine in Vera's system when she wakes up at 7:00 a.m., we can observe the pattern of the amount of medicine in her system at different hours. If we continue this pattern, we can see that the amount of medicine decreases each hour by multiplying it by 0.875. So, the amount of medicine at 7:00 a.m. would be:

7:00 p.m. - 306.25mg
8:00 p.m. - 306.25mg x 0.875 = 267.97mg
9:00 p.m. - 267.97mg x 0.875 = 234.47mg
10:00 p.m. - 234.47mg x 0.875 = 204.15mg
11:00 p.m. - 204.15mg x 0.875 = 178.48mg
12:00 a.m. - 178.48mg x 0.875 = 156.14mg
1:00 a.m. - 156.14mg x 0.875 = 136.21mg
2:00 a.m. - 136.21mg x 0.875 = 118.95mg
3:00 a.m. - 118.95mg x 0.875 = 103.97mg
4:00 a.m. - 103.97mg x 0.875 = 90.67mg
5:00 a.m. - 90.67mg x 0.875 = 78.89mg
6:00 a.m. - 78.89mg x 0.875 = 68.75mg
7:00 a.m. - 68.75mg x 0.875 = 60.06mg

Therefore, the approximate amount of medicine in Vera's system when she wakes up at 7:00 a.m. the next morning is 60.1mg (rounded to the nearest tenth).

Answer 2

61.68 mg

Step-by-step explanation:

Given the table :

5:00pm - 400mg

6:00pm - 350mg

7:00pm - 306.25mg

First we obtain the percentage rate at which the drug leaves her system per hour :

Take between 5-6 pm

((400 - 350) / 400) * 100%

(50 / 400) * 100%

0.125 * 100%

= 12.5%

.we can use the exponential function :

A = P(1 - r)^t

r = rate, t = time (hours) ; P= initial amount ; A = final amount

Mg of medicine left when she wakes up at 7:00 am

t = 7:00am - 5:00 pm = 14 hours

P = 400 mg

r = 0.125

A = 400(1 - 0.125)^14

A = 400 * 0.1542100

A = 61.68402913

About 61.68 mg