Answer: it will take 41.3 minutes
Step-by-step 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 = 120
t = 7 minutes
Since after 7 minutes, the amount of bacteria reduces by 0.5, then
y = 0.5 × 120 = 60
Therefore
60 = 120 × b^7
Dividing through by 120, it becomes
0.5 = b^7
Raising both sides of the equation by 1/7, it becomes
0.5^(1/7) = b^7/7
b = 0.9057
The equation becomes
y = 120(0.9057)^t
For the element to decay to 2 grams, then
2 = 120(0.9057)^t
2/120 = (0.9057)^t
0.0167 = (0.9057)^t
Taking log of both sides, it becomes
Log 0.0167 = tlog0.9057
- 1.777 = - 0.043t
t = - 1.777/- 0.043
t = 41.3 minutes
