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. \[ A(t)=5600\left(\frac{1}{2}\right)^{\frac{t}{14}} \] Find the amount of the sample remaining after 7 hours and after 60 hours. Round your answers to the nearest gram as necessary.

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.

Step 2 ：\[A(t)=5600\left(\frac{1}{2}\right)^{\frac{t}{14}}\]

Step 3 ：We are asked to find the amount of the sample remaining after 7 hours and after 60 hours. We can find this by substituting the given time values into the function $A(t)$ and calculating the result.

Step 4 ：For $t=7$ hours, substitute $7$ into the function $A(t)$ to get $A_7$.

Step 5 ：\[A_7 = 5600\left(\frac{1}{2}\right)^{\frac{7}{14}} = 3960\]

Step 6 ：For $t=60$ hours, substitute $60$ into the function $A(t)$ to get $A_{60}$.

Step 7 ：\[A_{60} = 5600\left(\frac{1}{2}\right)^{\frac{60}{14}} = 287\]

Step 8 ：Final Answer: The amount of the sample remaining after 7 hours is \(\boxed{3960}\) grams and after 60 hours is \(\boxed{287}\) grams.