a biologist has a 624 - gram sample of a radioactive substance. find the mass of the sample after two hours…

a biologist has a 624 - gram sample of a radioactive substance. find the mass of the sample after two hours if it decreases according to a continuous exponential decay model, at a relative rate of 14% per hour. do not round any intermediate computations, and round your answer to the nearest tenth.

a biologist has a 624 - gram sample of a radioactive substance. find the mass of the sample after two hours if it decreases according to a continuous exponential decay model, at a relative rate of 14% per hour. do not round any intermediate computations, and round your answer to the nearest tenth.

Answer

Explanation:

Step1: Identify the decay formula

The formula for continuous - exponential decay is $A = A_0e^{-rt}$, where $A_0$ is the initial amount, $r$ is the relative decay rate, and $t$ is the time. Here, $A_0 = 624$ grams, $r=0.14$ (since 14% = 0.14), and $t = 2$ hours.

Step2: Substitute the values into the formula

$A=624e^{-(0.14\times2)}$. First, calculate the exponent: $0.14\times2 = 0.28$. So, $A = 624e^{- 0.28}$. We know that $e^{-0.28}=\frac{1}{e^{0.28}}$. Using a calculator, $e^{0.28}\approx1.323129$. Then $\frac{1}{e^{0.28}}\approx\frac{1}{1.323129}\approx0.756$.

Step3: Calculate the final amount

$A = 624\times0.756$. $A=624\times0.756 = 471.744$. Rounding to the nearest tenth, $A\approx471.7$ grams.

Answer:

$471.7$ grams