Element X decays radioactively with half life of 15 minutes. If there are 870 grams of element X how long would it take the element to decay to 125 grams

Answer: it will take 42.1 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 = 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