May I have some help deciphering a word problem?

R

redsoxnation

New member
Joined
Mar 27, 2011
Messages
20
Yes, it's me again, hopefully posting in the right section.

I have a word problem that reads as follows: "Explain why the quadrupling time in exponential growth is just twice the doubling time. Then show that it's given by a "Rule of 140" analogous to the rule of 70."

I thought that "quadrupling time" referred to 2 to the fourth power (I'm sorry - I don't know how to write exponents here!), but that 's not working out for me. This seemed to be a simple request when I first read it; now I'm confused. And I do know what the Rule of 70 is, but the "Rule of 140" has me tripped up.

Can anyone decipher this? (a rhetorical question, to be sure)

Thanks again.
 
redsoxnation said:
I thought that "quadrupling time" referred to 2 to the fourth power

Nope. 8-)

To quadruple something means to get four times as much.


I don't know how to write exponents here!

We use the caret symbol (^) like this: 2^4 or e^(kt).

It's a shifted 6, on most keyboards.
Click to expand...

The basic model for exponential growth looks like the following.

A = A[sub:236y4cpp]0[/sub:236y4cpp] e^(kt)

Are you familiar with it?

Doubling time can be expressed by solving this equation for t:

2 A[sub:236y4cpp]0[/sub:236y4cpp] = A[sub:236y4cpp]0[/sub:236y4cpp] e^(kt)

Quadrupling time can be expressed by solving this equation for t:

4 A[sub:236y4cpp]0[/sub:236y4cpp] = A[sub:236y4cpp]0[/sub:236y4cpp] e^(kt)

Compare the two expressions for t, and then use a property of logarithms to demonstrate the answer.

 
mmm4444bot said:
The basic model for exponential growth looks like the following.

A = A0 e^(kt)

Are you familiar with it?
Click to expand...

No, I'm afraid I'm not familiar with that model. We've only been using y = I * (1 + r)^t. But I'm curious about the model you present. Could you break it down for me? I'll see if I can then plug in the number.

Thanks so much!
 


It's been awhile, since your last post; I hope that you came to understand the exercise and solution.

After solving those two equations (in my last post) for t, we get expressions for the times:

doubling time is ln(2)/k

quadrupling time is ln(4)/k

Using a property of exponents, ln(4) can be expressed as 2*ln(2).

This shows that the quadrupling time 2*ln(2)/k is twice the doubling time ln(2)/k.

 
mmm

Redsoxnation passed her course and posted a general thank you under odds and ends.
 
You must log in or register to reply here.
Top