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

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

step-by-step explanation: