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Delos · May 17, 2009, 09:32 AM

Hey,

Me again,

Ok so the is a= 15.3 x 0.88608860^t

And I have the value for a which is 7.65, how do I work out what t is? Please give me step by step explanation

thank you in advance..

DD

Perito · May 17, 2009, 09:41 AM

Me again,

Ok so the [something] is a= 15.3 x 0.88608860^t

And I have the value for "a" which is 7.65, how do i work out what "t" is?

Hi "Me".

$a= 15.3 \, \times \, 0.88608860^t$

$7.65 = 15.3 \, \times \, 0.88608860^t$

To find the power, you need to take the logarithm of both sides. It doesn't matter what the base of the logarithm is. It can be the common log (base 10), the natural log (ln = base e), or any other log.

$log(7.65)=log(15.3\, \times \, 0.88608860^t)$

$using\,\, log(a b) = log(a) + log(b)$

$log(7.65)=log(15.3) + log(0.88608860^t)$

$using\,\, log(a^b) = b \, log(a)$

$log(7.65)=log(15.3) + t\, log(0.88608860)$

$\frac {log(7.65)-log(15.3)}{log(0.88608860)}= t \,\approx\,5.73141$

galactus · May 17, 2009, 09:53 AM

$7.65=(15.3)\cdot .8860886^{t}$

$.5=.8860886^{t}$

$ln(.5)=tln(.8860886)$

$\frac{ln(.5)}{ln(.8860886)}=t\approx 5.732$

You have it correct, P, I just think you typoed at the end.

$\frac{log(7.65)-log(15.3)}{log(.886-886)}\approx 5.732$

Unknown008 · May 17, 2009, 09:58 AM

Yup, I got 5.73141006...

Perito · May 17, 2009, 10:05 AM

Me, too. I just have to quit falling asleep with "calculator".