Answer: it will take 42.1 minutes
Explanation:
We would apply the formula,
y = ab^t
Where
a represents the initial amount of bacteria.
t represents the half life.
From the information given
a = 870
t = 15 minutes
Since after 15 minutes, the amount of bacteria reduces by 0.5, then
y = 0.5 × 870 = 435
Therefore
435 = 870 × b^15
Dividing through by 870, it becomes
0.5 = b^15
Raising both sides of the equation by 1/15, it becomes
0.5^(1/15) = b^15/15
b = 0.955
The equation becomes
y = 870(0.955)^t
For the element to decay to 125 grams, then
125 = 870(0.955)^t
125/870 = (0.955)^t
0.144 = (0.955)^t
Taking log of both sides, it becomes
Log 0.144 = tlog0.955
- 0.841= - 0.019997t
t = - 0.841/- 0.019997
t = 42.1 minutes