Help with multipliers? (exponential stock-value growth)

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mallorymal

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John's stock is increasing exponentially. 2 years after he bought it, it was worth $450. Seven years after he bought it, it was worth $1250.

Okay, so I need to write an equation so he can find how much it was worth when he first bought it, but I need to find the multiplier first. How do I do that?
 
Re: Help with multipliers?

You can build two equations in two unknowns and solve for P(the initial amount) and k(the 'multiplier').

\(\displaystyle 450=Pe^{2k}\)

\(\displaystyle 1250=Pe^{7k}\)

Can you solve it?.
 
Re: Help with multipliers?

Well we recently started learning about logarithms so would that have anything to do with it? or do i just take the 2 root of 450 and the 7 root of 1250?
 
Re: Help with multipliers?

Of course, it's logs. What does 2 root of 450 mean?.
 
I got 21.21320344.
Or just 21.21.

and for the 7th root of 1250, I got 2.76959149.

I'm still confused though on what to do next. :?
 
mallorymal said:
I got 21.21320344....
Click to expand...
You "got 21.21320344..." for what? How? :shock:

Please reply with a clear listing of your work and reasoning so far. Thank you! :D

Eliz.
 
Like Stapel, I am having difficulty understanding where these roots are coing from. This is a logarithm problem, not roots.
 
Sorry about all that. I'm just really confused and not sure what I'm supposed to be doing.

So, do I have to use logs to find the multiplier or what. And if so how?
 
You could solve the first one for P and sub into the second one.

\(\displaystyle 450=Pe^{2k}\)

\(\displaystyle P=\frac{450}{e^{2k}}\).....[1]

Sub into second:

\(\displaystyle 1250=(\frac{450}{e^{2k}})e^{7k}=450e^{5k}\)

Now, solve for k. That's your multiplier. Then sub it back into [1] to find P.
 
galactus said:
You could solve the first one for P and sub into the second one.

\(\displaystyle 450=Pe^{2k}\)

\(\displaystyle P=\frac{450}{e^{2k}}\).....[1]

Sub into second:

\(\displaystyle 1250=(\frac{450}{e^{2k}})e^{7k}=450e^{5k}\)

Now, solve for k. That's your multiplier. Then sub it back into [1] to find P.
Click to expand...

In order to solve the first one, do you need to use logs? Or do you use logs later?
 
1250 = 450 * e^ (5k)

1250/450 = e^(5k)

25/9 = e^(5k)

use logs (natural log - ln) now.
 
mallorymal said:
Does the 5 come from the five years difference?
Click to expand...
The "5" comes from simplifying the division, using the rules for exponents.

From your questions, it sounds as though you have somehow missed out on some of the prerequisite material for this course. Are you familiar much with exponents? For instance, would you have any idea how to simplify "x[sup:15dqfdsm]7[/sup:15dqfdsm]/x[sup:15dqfdsm]2[/sup:15dqfdsm]"? Do you know what "exponential growth" means? Have you studied logarithms at all?

Thank you! :D

Eliz.
 
Oops. Okay, the 5 comes from subtracting the 7 and 2 because it's division (and you add if it's multiplication). :roll: Okay, so 1250/450 is 2.77. I took the 5th root of that and got 1.22. So, that's the multiplier? I hope so. :lol:
 
Please, forget about this root thing you seem to be stuck on.

You have \(\displaystyle 1250=450e^{5k}\)

\(\displaystyle \frac{25}{9}=e^{5k}\)

Take ln of both sides:

\(\displaystyle ln(\frac{25}{9})=5k\)

\(\displaystyle k=\frac{ln(\frac{25}{9})}{5}=\frac{2ln(\frac{5}{3})}{5}\approx{.20433....}\)

Sub into P, \(\displaystyle P=\frac{450}{e^{2(.20433)}}\approx{299.04}\)

See?. Now, you really should see your instructor if you are lost regarding any of the steps I showed you.

Best wishes.
 
The only thing I don't understand is what ln means. I've never heard of it. But other than that I understand the rest.
 
It will be ver useful if you sat down with your teacher and go through the solution and ask questions.

This is a very important topic for next level of mathematics - you need to understand logarithm and exponentials very clearly.
 
Different way:

Let P be initial value, R be return rate.

450 = P*(1+R)^2

1250=P*(1+R)^7

Using second equation divide by the first equation to cancel P:

1250/450 = (1+R)^7/(1+R)^2

25/9=(1+R)^5

Take 5th root on both sides:

1+R =(25/9)^(1/5) = 1.2267

Using first equation :

P = 450/(1+R)^2

=450/1.2267^2

=299

The answer is $299
 
For some reason, I was under the impression you had to use logs. mathispowerful posted a good solution using the root method you kept wanting to use. I am sorry for being presumptutous.
 
galactus said:
For some reason, I was under the impression you had to use logs. mathispowerful posted a good solution using the root method you kept wanting to use. I am sorry for being presumptutous.
Click to expand...
The exercise involved exponential growth, which implied (in the solution) using logs. And the poster clearly stated that the class had begun studying logs, so the use of logs made sense. Since the poster never replied saying what was understood nor showing any work, assumptions (and presumptions) were required of you. :shock:

This highlights why clear feedback from the students, with the students showing their work, is often crucial. It's hardly your fault that this wasn't provided. :wink:

Eliz.
 
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