# Exponential Growth and Decay

• May 20th 2011, 08:46 PM
MathsBeforeBedtime
Exponential Growth and Decay
Hi, This is my first post, i couldn't find a proper category for my topic, so I'll post it here. having troubles understanding these questions...

I have attached the two questions... thanks. They use the Q = Qo*e^kt and Q = Qo*e^-kt formula structures. Thank you very much in advance.

http://i.imgur.com/uFEqm.jpg
• May 20th 2011, 09:44 PM
pickslides

$\displaystyle Q = Q_0e^{kt}$

Substitute the points $\displaystyle (0, Q_0)$ and $\displaystyle \left(1600, \frac{Q_0}{2}\right)$

What do you get?
• May 22nd 2011, 12:16 AM
MathsBeforeBedtime
Quote:

Originally Posted by pickslides

$\displaystyle Q = Q_0e^{kt}$

Substitute the points $\displaystyle (0, Q_0)$ and $\displaystyle \left(1600, \frac{Q_0}{2}\right)$

What do you get?

um sorry? where did you get points from? I've never been taught to get points for these questions?
• May 22nd 2011, 12:36 AM
pickslides
I found these points from you question.

At t=0 the amount of radioactive material is $Q_0$ , is this clear why?

Now the meaning of half life is the time taken for the radioactive material to reduced to half of its original self.

From the question, when t=1600 then the initial amount is halved i.e $\frac{Q_0}{2}$
• May 22nd 2011, 03:23 AM
MathsBeforeBedtime
Quote:

Originally Posted by pickslides
I found these points from you question.

At t=0 the amount of radioactive material is $Q_0$ , is this clear why?

Now the meaning of half life is the time taken for the radioactive material to reduced to half of its original self.

From the question, when t=1600 then the initial amount is halved i.e $\frac{Q_0}{2}$

ohk, makes sense now, will give it a try. thanks
• May 22nd 2011, 05:05 AM
pickslides
Quote:

Originally Posted by MathsBeforeBedtime
ohk, makes sense now, will give it a try. thanks

Good to hear, let us know how you go.
• May 23rd 2011, 03:03 AM
MathsBeforeBedtime
Quote:

Originally Posted by pickslides
Good to hear, let us know how you go.

turns out I didn't get it. my tutor said for part a), do 500 / 1600 to get 0.3125 = 31%, then just do 50% - 31% = 19%

for part b) my tutor said to go from 100% to 50% that's a half life so it = 1600 years, then to go from 50 to 25% that's another 1600 years and so now we are at 75%. 1600 + 1600 = 3600 years.

turns out you didn't need to use the formula for this question, bit weird. but makes kinda sense this way.

qs 14 I do not know.