Question

Initially 100 milligrams of a radioactive substance was present. After 6 hours the mass had decreased by 2%. If the rate of decay is proportional to the amount of the substance present at time t, find the amount remaining after 24 hours. (Round your answer to one decimal place.

Answer 1

The amount of radioactive material remaining after 24 hours is 92.15 kg.

Exponential function

An exponential function is in the form:

y = abˣ

where y, x are variables, a is the initial value of y and b is the multiplier.

Let y represent the amount of the substance after t hours.

From the equation, a = 100 mg

Also, after 6 hours:

$100-100*2\%=100b^6\\\\98=100b^6\\\\b=0.9966$

After 24 hours:

y = 100(0.9966)²⁴ = 92.15 kg

The amount of radioactive material remaining after 24 hours is 92.15 kg.

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