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

Initial amount is 523 grams

Amount after 100 years is 52 grams

Step-by-step explanation:

General exponential function for radioactive substances is given by

A(t) = Ao(1/2)^t/t1/2

Where,

A(t) is the amount remaining after t years

Ao is the initial amount of the radioactive substance

t is the number of years required for the radioactive substance to decay to A

t1/2 is the half-life of the radioactive substance

Comparing A(t) = 523(1/2)^t/30 with the general exponential function

Initial amount (Ao) = 523 grams

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

t = 100

A(100) = 523(1/2)^100/30 = 523×0.5^3.333 = 523×0.0992 = 51.8816 = 52 grams (to the nearest gram)