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