The age of a rock is determined by the function, A (t) = A 0 e - 0.000002t, where Isotope Q, with an initial value of A 0, decays at a constant rate 0.000002 per year, for a number of years (also known as the age of the rock), t. A sample originally has 80 grams of Isotope Q, decays, and now has 20 grams of the isotope. Determine the current age of the sample, in years. Round your answer to the nearest thousand years. Make sure to include the correct place value commas in your answer.

Question

Lamont Summers

Mathematics

22 July, 20:20

The age of a rock is determined by the function, A (t) = A 0 e - 0.000002t, where Isotope Q, with an initial value of A 0, decays at a constant rate 0.000002 per year, for a number of years (also known as the age of the rock), t. A sample originally has 80 grams of Isotope Q, decays, and now has 20 grams of the isotope. Determine the current age of the sample, in years. Round your answer to the nearest thousand years. Make sure to include the correct place value commas in your answer.

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Jocelyn Marshall · Answer 1

A (t) = A 0 e - 0.000002t

A (t) 20

A0. 80

T time in years?

20=80 e - 0.000002t

Solve for t

20/80=e - 0.000002t

Log (20/80) = log (e) * - 0.000002t

T = (log (20:80) : log (e)) : (-0.000002)

T=693,147 years