Certain radioactive material decays in such a way that the mass remaining after $t$ years is given by the function
\[
m(t)=370 e^{-0.045 t}
\]
where $m(t)$ is measured in grams.
(a) Find the mass at time $t=0$.
Your answer is
(b) How much of the mass remains after 25 years?
Your answer is
Answer
Final Answer: (a) The mass at time \(t=0\) is \(\boxed{370}\) grams. (b) The mass remaining after 25 years is approximately \(\boxed{120.12}\) grams.
Step 1 ：The problem provides the function \(m(t)=370 e^{-0.045 t}\) which gives the mass remaining after \(t\) years.
Step 2 ：To find the mass at time \(t=0\), we substitute \(t=0\) into the function, which gives us \(m(0)=370 e^{-0.045 \times 0} = 370\) grams.
Step 3 ：To find the mass remaining after 25 years, we substitute \(t=25\) into the function, which gives us \(m(25)=370 e^{-0.045 \times 25} \approx 120.12\) grams.
Step 4 ：Final Answer: (a) The mass at time \(t=0\) is \(\boxed{370}\) grams. (b) The mass remaining after 25 years is approximately \(\boxed{120.12}\) grams.
