The remaining mass mass of the substance at time t can be modeled with an exponential equation in this form:
m = ab^t,
where m is the remaining mass in grams, and t is the time in days.
We are given the mass at time zero and at time two.
Let t = 0.
10 = ab^0
a = 10
m = 10b^y
Let t = 2.
7 = 10b²
b² = 0.7
b ≈ 0.84
m ≈ 10(0.84)^t
Now to find the half-life, let m = 5 g, which is half of the initial mass. Solve for t.
5 = 10(0.84)^t
(0.84)^t = 0.5
t ln(0.84) = ln(0.5)
t = ln(0.5) / ln(0.84) ≈ 3.9 days
