Mathematics: You have 900-grams of an an unknown radioactive substance that has been determined to decay according to d ( t ) = 900 e − 0.002415 ⋅ t d ( t ) = 900 e - 0.002415 ⋅ t where t t is in years. how long before half of the initial amount has decayed? it will take __ years for half of the initial amount to decay. (round to 1 decimal place)

You have 900-grams of an an unknown radioactive

Ответ:

lily24113

13.03.2022

Now, the initial amount is 900 grams, so half of that will be 450 grams.

so, how long will it be, for D(t) to turn to 450 grams?

$\bf D(t)=900e^{-0.002415t}\implies 450=900e^{-0.002415t}
\\\\\\
\cfrac{450}{900}=e^{-0.002415t}\implies \cfrac{1}{2}=e^{-0.002415t}\\\\
-------------------------------\\\\
\textit{Logarithm Cancellation Rules}\\\\
log_{{ a}}{{ a}}^x\implies x\qquad \qquad 
{{ a}}^{log_{{ a}}x}=x\\\\
-------------------------------\\\\$

$\bf log_e\left( \frac{1}{2} \right)=log_e\left( e^{-0.002415t} \right)\implies log_e\left( \frac{1}{2} \right)=-0.002415t
\\\\\\
\cfrac{ln\left( \frac{1}{2}\right)}{-0.002415}=t\implies 287.0174661 \approx t$

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Ответ:

kmontello5

03.11.2021

Mathematics

2.05

Step-by-step explanation:

because you have to divide

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