The radioactive substance uranium- 240 has a half-life of 14 hours. The amount $A(t)$ of a sample of uranum-240 remaining (in grams) after $t$ hours is given by the following exponential function. \[ A(t)=5600\left(\frac{1}{2}\right)^{\frac{t}{14}} \] Find the initial amount in the sample and the amount remaining after 60 hours. Round your answers to the nearest gram as necessary. \begin{tabular}{|c|c|} \hline Initial amount: & Dgrams \\ \hline Amount after 60 hours: & Dgrams \\ \hline & $x$ \\ \hline \end{tabular}

Step 1 ：The radioactive substance uranium-240 has a half-life of 14 hours. The amount \(A(t)\) of a sample of uranium-240 remaining (in grams) after \(t\) hours is given by the following exponential function: \[A(t)=5600\left(\frac{1}{2}\right)^{\frac{t}{14}}\]

Step 2 ：The initial amount of the sample can be found by evaluating the function at \(t=0\).

Step 3 ：Substitute \(t=0\) into the function: \[A(0)=5600\left(\frac{1}{2}\right)^{\frac{0}{14}} = 5600\]

Step 4 ：So, the initial amount of the sample is \(\boxed{5600}\) grams.

Step 5 ：The amount remaining after 60 hours can be found by evaluating the function at \(t=60\).

Step 6 ：Substitute \(t=60\) into the function: \[A(60)=5600\left(\frac{1}{2}\right)^{\frac{60}{14}} = 287\]

Step 7 ：So, the amount remaining after 60 hours is \(\boxed{287}\) grams.