The radioactive substance cesium-137 has a half-life of ? 75. The amount $A(i)$ (in grams) of a sample of cesium-137 remaining after $t$ years is given by the following exponential function. \[ A(t)=458\left(\frac{1}{2}\right)^{\frac{1}{30}} \] Find the initial amount in the sample and the amount remaining after 100 years. Round your answers to the nearest gram as necessary. \begin{tabular}{l} Initial amount: \\ Amount after 100 years: \\ \hline \\ \hline \end{tabular}

Step 1 ：The initial amount is the amount of the substance at time t=0. So, we need to substitute t=0 into the function to find the initial amount. The amount remaining after 100 years is found by substituting t=100 into the function. We then round the results to the nearest gram.

Step 2 ：Substitute t=0 into the function \(A(t)=458\left(\frac{1}{2}\right)^{\frac{1}{30}}\), we get the initial amount is 458 grams.

Step 3 ：Substitute t=100 into the function \(A(t)=458\left(\frac{1}{2}\right)^{\frac{1}{30}}\), we get the amount remaining after 100 years is 45 grams.

Step 4 ：Final Answer: The initial amount of the sample is \(\boxed{458}\) grams and the amount remaining after 100 years is \(\boxed{45}\) grams.