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I am currently working my way through Hughes-Hallet et al., Calculus- Single and Multivariable.

I am having trouble with the following problem.

Show algebraically that if $P=P_0a^t$ doubles between time $t$ and time $t + d$, then $d$ is the same number for any $t$.

I have started by writing out two equations.

$$ P=P_0 a^{t}$$

$$ 2P=P_0a^{(t+d)}$$

Not sure where to go from here.

Iceman
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A nobody
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1 Answers1

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$P=P_o a^{t}$ .... (1)

$2P=P_oa^{(t+d)}$ .... (2)

If we divide (2) by (1) and simplify, we will get $d = {log(2) \over log(a)}$ , which is constant if a is given as constant.

Mick
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