Question

The radioactive substance cesium-137 has a half-life of 30 years. The amount A(t) (in grams) of a sample of cesium -137 remaining after t years is given by the following exponential function.A (t) = 523 (1/2)^t/30Find the initial amount in the sample and the amount remaining after 100 years.Round your answers to the nearest gram as necessary.Initial amount:Amount after 100 years:

Answer 1

After 100 years:

Replace t by 100:

A (t) = 523 (1/2)^t/30

A (100) = 523 (1/2)^100/30 = 523 (1/2) ^10/3 = 51.88 =52 grams

The initial amount of the sample is 523