Question

question a certain radioactive material decays in such a way that the mass in kilograms remaining after t years is given by the function m(t)=120e^(-0.018t) how much mass remains after 50 years? round to 2 decimal places. provide your answer below:

Explanation:

Step1: Substitute t = 50 into the function

Substitute $t = 50$ into $m(t)=120e^{- 0.018t}$, we get $m(50)=120e^{-0.018\times50}$.

Step2: Calculate the exponent value

First, calculate $-0.018\times50=-0.9$. So $m(50)=120e^{- 0.9}$.

Step3: Calculate the exponential - function value

We know that $e^{-0.9}\approx0.40657$. Then $m(50)=120\times0.40657$.

Step4: Calculate the final mass

$120\times0.40657 = 48.7884$. Rounding to 2 decimal places, we get $m(50)\approx48.79$.

Answer:

$48.79$