college algebra

Question

Mercury 197 has a decay rate of 1.066% per hour. Given the exponential model representing the amount of Mercury 197 remaining after t hours, find how long it will take 387 grams of the Mercury 197 to decay to 38 grams. Round your result to the nearest thousandth hour.

A(t) = A0eln(0.98934)t

Answer 1

Hello, Janichkis, thank you for taking the time to post your question!

You have the correct general form of the exponential model that you want to use for this one identified

A(t) = A0*e^ln(0.98934)t

The next step then is to plug in the values that we know from the information given to us in the question

38 = 387 * e^ln(0.98934)t

to solve for t then you want to divide both sides by 387 and then take the natural log of both sides

ln(38/387) = ln(0.98934)t

then solve for the value of t

t = ln(38/387) / ln(0.98934)

t = 216.567

that means that it takes about 216.567 hours for 387 grams of Mercury 197 to decay down to 38 grams

I hope that helps! :)