Natural growth question (1 Viewer)

[kpad5991]

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?

 

[fan96]

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

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

Then, the cost after months is given, as a percentage of the initial cost, by .

will give the cost after 12 months as a percentage of the original. Subtract from it to get the increase in percentage cost.

The time required for the cost to double can be found by setting and solving for .