Question

The radioactive substance uranium -240 has a half-life of 14 hours. The amount A(t) of a sample of uranium -240 t hours is given by the following exponential function. A(t)=3900((1)/(2))ᵗ/(14)) Find the initial amount in the sample and the amount remaining after 50 hours. Round your answers to the nearest gram as necessary.

Answer 1

The initial amount in the sample is 3900 grams. The amount remaining after 50 hours is approximately 79.56 grams.

Step-by-step explanation:

To find the initial amount in the sample, substitute t = 0 into the exponential function A(t). A(t) = 3900(1/2)^(t/14). A(0) = 3900(1/2)^(0/14) = 3900(1/2)^0 = 3900(1) = 3900 grams.

To find the amount remaining after 50 hours, substitute t = 50 into the exponential function A(t). A(t) = 3900(1/2)^(t/14). A(50) = 3900(1/2)^(50/14) ≈ 3900(0.0204) ≈ 79.56 grams.