[ Read] Physics Realted Math Questions, Please some Advice

[Tommis]

Hello,

I am seeking some quick advice for these two problems I have on this physics homework I am completing right now. Please look below. There are 2 questions.

1. The population of a country doubles every 24 years. How long will it take for the populartion to increase by a factor of 5?

2. The 1970 earthquake in Peru registered 7.7 on the Richter scale. How much more intense was this earthquake compared to the tremor in Ontario in 2002 that was measuered to be 5.2 on the Richter scale?

I have a test coming up and I need to know how to solve these questions. Regarding #2 it is going to use log's. For example a earthquake at a scale of 4 is 10 times more intense than one at a scale of 3. (On the Richter scale).

Any help would be GREATLY appreciated. Thank you very, very much in advance.

Cya,
Tommis

 

[mikelepore]

Question 1: Suppose, instead of the population increasing by a factor of 5, a different problem had asked about a population increasing by a factor of 8. Three doubling (times 2) steps would be needed to reach 8: step from 1 to 2, step from 2 to 4, step from 4 to 8. How are the numbers 2, 3, and 8 related?

 

[Tommis]

Hey,

"How are the numbers 2, 3, and 8 related?"

I am not sure, from thoes numbers you told me, I can see no pattern. Do you mean 2, 4, and 8? I could understand thoes, they are double each time.

And yes, I have been trying to put the first question into a equation form, but I couldn't get it just because of the fact that its the NEW number that doubles.

How would it be done?

Cya,
Tommis

 

[Tommis]

Hey,

Bump.

Any ideas? Any help would be appreciated.

Cya,
Tommis

 

[CrazyIvan]

Hey,
"How are the numbers 2, 3, and 8 related?"

I am not sure, from thoes numbers you told me, I can see no pattern. Do you mean 2, 4, and 8? I could understand thoes, they are double each time.

$$\overbrace{2 \times 2 \times 2}^{3 times} = 8$$

 

[Tommis]

Hey,

Yes, I understand that fully. :P Just how could I do that with the question now?

Cya,
Tommis

 

[CrazyIvan]

Do you know of a way to express the population as a function of time?

 

[kenewbie]

Ok. I want to jump in here and try to see if I can figure it out. I'm a regular scrub so Tommis please don't accept this as the answer. If I do something wrong, I'd appreciate it if someone can point it out to me.
--

How do you express a value that doubles X times?

original value V = 2
the double of V = 2 * 2 = 4
the double of 4 = 4 * 2 = 8
the double of 8 = 8 * 2 = 16

V * 2^0 = 2
V * 2^1 = 4
V * 2^2 = 8
V * 2^3 = 16

So, to get a value V that has doubled X times, I guess you can write that as V * 2^x-1.

You need a factor of 5. How big must X be for 2^x to reach 5?

5 = 2^x
log 5 = x * log 2
x = log 5 / log 2
x ~= 2.32

So, after doubling 2.32 times, the original value should be 5 times as large. It takes 24 years to double, so 24 * 2.32 ~= 55.7 years.

A quick control: If we double 1 2.32 times we should get 5.. 1 * 2^2.32 = 4.99 ~= 5.

The second question seems to escape me at the moment.

k

 

[mikelepore]

That's correct. I was thinking of: just as 2^3=8, or log to the base 2 of 8 is 3, similarly, log to the base 2 of 5 is whatever -- but I couldn't remember how to get the number.