\"Let P(t) be the total petroleum on earth t years since 1900. This includes all

Question

"Let P(t) be the total petroleum on earth t years since 1900. This includes all petroleum, including what hasn't been discovered yet. No new petroleum is made. P is measured in millions of barrels. What are the units of P'(t)? What is the meaning of P'(t)? What is its sign? What about the secons derivative? How would you set out estimating P'(100) and P'(114)? What about P''(t) at those two years?"

I said the units of p'(t) are barrels/year which is the decrease in quantity of barrels per year. The sign for f'(x) and f"(x) should be negative, right?
As for estimating P'(t), I think I need to know the amount of petroleum started with and the amount consumed per year. However, I am not sure how to estimate P"(t).

Explanation / Answer

The units of P'(t) are barrels/year, where P'(t) denotes the rate of change of petroleum per year(time ' t ') that is dP/dt.

Basically, we need a function P(t) to denote the total petroleum on the earth. According to your information, P'(t) is always negative because the petroleum is using every year and it is decreasing quantity. Notie that P'(100) and P'(114) denote the petrolem decreasing at the rate per year at 100 and 114 the year respectively. P''(t) used to determine in which year the maximum usage of petroleum or minumum usage or simply to get the absolute values of P(t).

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