Dear all, I am a high school student & I have the following problem which to me it is very confusing.

Thank you very much!

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- Mar 19th 2008, 05:53 PM #1

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- Mar 19th 2008, 05:58 PM #2
(a) this is a separable differential equation.

you want to solve $\displaystyle R' = kR$

rewrite as $\displaystyle \frac {R'}R = k$

now integrate both sides and continue (don't forget the arbitrary constant). use the clues given in the question to solve for the unknown.

(b) once you answered part (a), plug in $\displaystyle R = 10$ and solve for $\displaystyle t$

(c) $\displaystyle kt_h = \ln 2$, always

here $\displaystyle t_h$ is the half-life, $\displaystyle k$ is the rate of decay.

- Mar 19th 2008, 06:00 PM #3
$\displaystyle \frac{dR}{dt}=kR \iff \frac{dR}{r}=kdt$ so integrate both sides

$\displaystyle \int \frac{dR}{R}= \int kdt \iff ln(R)=kt+c$

solveing for R

$\displaystyle R=e^{kt+c}=e^{kt} \cdot e^c=Ae^{kt}$

$\displaystyle R(t)=Ae^{kt}$

$\displaystyle R(0)=10^6=Ae^{0}$

You should be able to finish from here.

Good luck.

- Mar 19th 2008, 07:11 PM #4

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- Mar 19th 2008, 07:35 PM #5

- Mar 20th 2008, 07:00 AM #6

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