Question

certain radioactive material decays in such a way that the mass remaining after \\(t\\) years is given by the function
\\m(t) = 365e^{-0.01t}\\
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 40 years?
your answer is
round answers to 1 decimal place.

Explanation:

Step1: Find mass at \(t = 0\)

$$m(0) = 365e^{-0.01(0)} = 365e^{0} = 365$$

Step2: Round to one decimal place

$$m(0) \approx 365.0$$

Step3: Find mass at \(t = 40\)

$$m(40) = 365e^{-0.01(40)} = 365e^{-0.4}$$

Step4: Calculate the value

$$m(40) \approx 365 \times 0.67032 = 244.6668$$

Step5: Round to one decimal place

$$m(40) \approx 244.7$$

Answer:

(a) 365.0
(b) 244.7