Question

25.06/25.02=a^(.03)
How do I convert the exponent. If the exponent was a 3 I know I could multiply both sides by (1/3). But this decimal is messing me up. haha
Thanks!

Answer 1

if the decemel was 3 you could multiply both sides by 1/3 ?

Answer 2

you can solve this with logs

Answer 3

Can also convert 0.03 to the fraction 3/100 and use exponent rules.

Answer 4

zzRock If the Exponent was 3
We aren't up to the logs section yet thats why I don't want to use logs.

Answer 5

I'd be curious to see from zzrocker how to do this with logs since we're solving for the base and not the exponent.

Answer 6

My reasoning is that if you wanted to solve
\[A=x^2 \rightarrow x=A^{1/2}\]
Likewise, if
\[A=x^{1/2} \rightarrow x=A^2\]
So, if
\[K=a^{3/100} \rightarrow a=K^{100/3}\]

Answer 7

(This is all assuming no negative numbers and no complex numbers)

Answer 8

So I'm sure when you said, " If the exponent was a 3 I know I could multiply both sides by (1/3)" you meant that you could raise both sides to the exponent 1/3. That is correct.
Here, the exponent is 3/100, so exponentiate both sides to the 100/3.

Answer 9

OK thanks Cliff

Answer 10

And yes raise to the power of (1/3) in my example :)

Answer 11

Let me know what you get as your answer. I got something close to 1.05

Answer 12

Yes I got 1.055. Now I am supposed to use this to figure out the growth rate.
So f(.05)=25.06
I will be using Q=Q0a^t
25.06=Q0(1.055)^.05
So when I do (1.055)^.05 I get 1.003
Then I 25.06/1.003 to get 24.993. But thats supposed to be percentage growth rate so 2499%?!

Answer 13

Not sure if I know what you mean. A percent increase from 25.02 to 25.06, or do you want the growth factor? And what does that .05 mean?

Answer 14

t would be x
P is an exponential function of t with base a

Answer 15

Ah, ok, so t=0.05 is like .05 seconds or .05 days or something like that?

Answer 16

Ok, I think I followed your above steps.
First of all, Is your function f(t)=Q0*a^t or Q0*a^(kt)?
Secondly, if you divide 25.06 by (1.055)^0.05 you are solving for Q0, right?

Answer 17

If you're looking for percentage increase then it depends on how you want to express that.
You can say that 25.06 is 25.06/Q0 times as large as Q0, or you can say the amount of increase (25.06 - Q0) is [(25.06 - Q0)/Q0]*100% more than Q0..

Answer 18

here is the original problem
f(.02)=25.02 and f(.05)=25.06

Answer 19

I just want to make sure I have any idea what is going on maybe I am screwing it up somewhere

Answer 20

I see. f(.02)=25.02 and f(.05)=25.06 was the given information and the question is "what is the growth rate?"

Answer 21

Then I think you should probably start over.

Answer 22

You missed the growth rate variable from your original equation. I think that is what you are supposed to solve for. You may need logarithms afterall.

Answer 23

does a^.03 change into 1/.03 to get rid of exponent?
becuase a^3 would be 1/3 to get rid of the exponent

Answer 24

Neither. The equation you need to start with is
\[f(t)=P_0e^{rt}\]
Your task is to solve for r.

Answer 25

I hope I'm understanding your question right because this will require logarithms, and you said that you didn't want to use logs.

Answer 26

They are using P=P0a^t in the book
I can do the problem if it isn't a decimal for t! lol

Answer 27

Ok, so it's replacing e^r with a, I see..

Answer 28

Hmm, then what you did is fine, that gets you a, but then I'm not sure what it means by find growth rate if you're not finding r.

Answer 29

ok thanks Ill get help on it tomorrow

Answer 30

1.5 hours is enough on one problem when I can do the others so easily its really irritating

Answer 31

Ok, you can still get the growth rate, r from here, but you still need to use logarithms.
Understood. Leave it alone for now and reread it with a fresh mind.