ASAP
Element X decays radioactively with a half life of 7 minutes. If there are 120 grams of Element X, how long, to the nearest tenth of a minute, would it take the element to decay to 2 grams?

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

a. 19,958,400

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