# rate question

• November 16th 2008, 05:34 PM
Craka
rate question
Question asks to find the rate of atmospheric pressure changing for a rocket rising vertically at 5km/s when at an altitude of 1km.
Given the relationship of atmospheric pressure (in milibars) at an altitude of x kilometres is given by 1000(0.88)^x.

I just can't see how to differentiate the function. Anyone?
• November 16th 2008, 05:37 PM
skeeter
integrate?

the question is asking for a rate of change ... sounds like a derivative to me.
• November 16th 2008, 05:43 PM
Craka
Sorry yes I meant differentiate, I cannot see how to differentiate it.
• November 16th 2008, 06:14 PM
skeeter
$\frac{d}{dt} a^x = a^x \cdot \ln{a} \cdot \frac{dx}{dt}$
• November 16th 2008, 07:12 PM
Craka
Is this right?
$
\begin{array}{l}
\frac{d}{{dt}}P(x) = \frac{d}{{dt}}[1000(0.88)^x ] \\
= 0.88^x \ln (0.88)\frac{{dx}}{{dt}} \\
\end{array}
$
• November 16th 2008, 08:44 PM
Craka
Is this right?
$
\begin{array}{l}
\frac{d}{{dt}}P(x) = \frac{d}{{dt}}[1000(0.88)^x ] \\
= 0.88^x \ln (0.88)\frac{{dx}}{{dt}} \\
\end{array}
$
• November 17th 2008, 05:25 PM
skeeter
what happened to the constant 1000?