QuestionCertain radioactive material decays in such a way that the mass remaining after $t$ years is given by the function $$m(t)=450 e^{-0.01 t}$$ where $m(t)$ is measured in grams. (a) Find the mass at time $t=0$.
Your answer is $\square$ (b) How much of the mass remains after 50 years?
Your answer is $\square$

Studdy Solution
Simplify the expression:
$$m(50) = 450 e^{-0.5}$$
Calculate $e^{-0.5}$ using a calculator or a known approximation:
$$e^{-0.5} \approx 0.60653$$
Therefore:
$$m(50) = 450 \times 0.60653$$
$$m(50) \approx 273$$
The mass remaining after 50 years is approximately:
$$\boxed{273}$$