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.=At45812t30Find the initial amount in the sample and the amount remaining after 50 years.Round your answers to the nearest gram as necessary.Initialamount: gramsAmountafter50years: grams

The formula for the amount of a radioactive substance remaining after a certain amount of time is given by the equation:

At = A0 * (1/2)^(t/h)

where: At is the amount of the substance remaining after time t, A0 is the initial amount of the substance, t is the time that has passed, and h is the half-life of the substance.

In this case, the equation given is At = 458 * (1/2)^(t/30).

To find the initial amount (A0), we need to find the amount of the substance at time t=0. Substituting t=0 into the equation gives:

A0 = 458 * (1/2)^(0/30) = 458 * (1/2)^0 = 458 * 1 = 458 grams

So, the initial amount of the substance is 458 grams.

To find the amount remaining after 50 years, we substitute t=50 into the equation:

At = 458 * (1/2)^(50/30)

This simplifies to approximately 183 grams when rounded to the nearest gram.

So, the initial amount of the substance is 458 grams and the amount remaining after 50 years is 183 grams.