# Thread: Natural growth question

1. ## Natural growth question

The cost C of an article is rising with inflation in such a way that at the start of every month, the cost is 1% more than it was a month before. Let C0 be the cost at time zero.

a) I figured out that C= C0 x1.01^t. The question is find the percentage increase in the cost over 12 months.

b) I figured out that C=C0e^kt and k=ln1.01 given t=1, C=1.01C0. But how do you find the
I) percentage increase in the cost over twelve months?
II) the time required for the cost to double?

2. ## Re: Natural growth question

Unless the question specifically asks for it, it's not necessary to use $e$ here.

Let the initial cost $C_0$ be $100\%$, or $1$. We don't actually need to know what the initial cost is, we're only interested in its percentage change.

Then, the cost $C_t$ after $t$ months is given, as a percentage of the initial cost, by $C_t = 1.01^t$.

$C_{12}$ will give the cost after 12 months as a percentage of the original. Subtract $100\%$ from it to get the increase in percentage cost.

The time required for the cost to double can be found by setting $C_t = 2$ and solving for $t$.

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