A patient receives 10 mL of medicine every day at the same time. If 50% of the medicine metabolizes during the day, how much medicine will be left in his body after 3 days?

Question

plz help me, thank you so much!!

Answer 1

The formula takes into account the amount of medicine in his body AFTER the third day. So, we need to calculate each days injection and absorption rate daily. The general formula would be

Symbols

D= Days = 3

R = Metabolism rate = 0.5

10ml is the daily injection

First day injection after D days metabolism = 10ml x (R raised to D)

Second day injection after D-1 days metabolism = 10ml x (R raised to D -1)

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Last day injection with 1 day metobolism = 10ml x (R raised to 1) or simply 10ml x R

Final answer = Add up all the previous days calculations

So here we are given three days, 10ml each day and 0.5 metabolism after each day

First day injection after 3 days = 10ml x 0.5 (R) raised to 3 (D days) or cubed = 10 x 0.5 x 0.5 x 0.5 = 10 x 0.125 = 1.25ml

Second day injection after 2 days = 10ml x 0.5 (R) raised to 2 (D-1) or squared = 10ml x 0.5 x 0.5 = 10 x 0.25 = 2.50ml

Third day injection after 1 day = 10ml x 0,5 (R) raised to 1 (D-2) = 10ml x 0.5 = 5ml

Final answer = 1.25ml + 2.50ml + 5.00ml = 8.75ml

Answer 2

On the first day, he takes the first 10mL.

Day One: 10mL

When he goes to take the medicine on the second day, 50% (5mL) has already been metabolized. He now takes the day two medicine.

Day Two: 5mL + 10mL = 15mL

When he goes to take the medicine on the third day, 50% (7.5mL) has already been metabolized. He now takes the day three medicine.

Day Three: 7.5mL + 10mL = 17.5mL

Answer 3

Each day he has half than the day before: 10 * 0.5 * 0.5 * 0.5 = 1.25 ml