Question

A scientist has 50 grams of a radioactive element. The amount of radioactive element remaining after t days can be determined using the equation mc013-1.jpg. After two days the scientist receives a second shipment of 50 grams of the same element. The equation used to represent the amount of shipment 2 remaining after t days is mc013-2.jpg. Which of the following is an equivalent form of the expression for the amount remaining in shipment 2?
mc013-3.jpg
mc013-4.jpg
mc013-5.jpg
mc013-6.jpg

Answer 1

Shipment 2 (arriving at t = 2) is 50(1/2)^{t-2}. Rewrite:

50(1/2)^{t-2} = 50(1/2)^t(1/2)^{-2} = 50(1/2)^t·2^2 = 200(1/2)^t.

So the equivalent form is 200(1/2)^t.