Ascientist begins with 100 milligrams of a radioactive substance that decays exponentially. after 33 hours, 50 mg of the substance remains. how many milligrams will remain after 59 hours? (round your answer to two decimal places.)

Explanation:

Radioactive decay behaves according to the law of exponential decay:

Where:

So we need to find the decay rate r. Let's find it using the equation and the data provide, but first, we need to convert the hours in days:

Now for then:

Divide both sides by 100:

Take the natural logarithm of both sides:

Multiply both sides by -8/11:

Now we have found the rate decay r, let's find how many milligrams will remain after 59 hours (25/12 day):

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