Question

a substance decays 18℅ each day. after 11 days, there are 13 milligrams of the substance remaining. how many milligrams were there initially? round to two decimals

Answer 1

The decay formula is as follows:
M(t)=M(0)((1-r)^t)
where
M(t)=mass of substance after t days
r=rate of decay

Substitute r=0.18, t=11, we get
M(11)=M(0)(1-0.18)^11
=>
M(0)=(13 mg) / (0.82^11) = 115.34 mg (initial mass of substance)

Answer 2

The amount remaining (Q(t)) can be expressed in terms of the initial quantity Q₀ and the number of days (t) by
Q(t) = Q₀×0.82^t

Filling in the given numbers, you have
13 = Q₀×0.82^11
13/0.82^11 = Q₀
Q₀ ≈ 115.34 . . . . milligrams