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2 years ago

It is estimated that world reserves of oil currently stand at 2625

Mathematics

1 answer:

seraphim [82]2 years ago

4 0

Answer:

35.4 years

Step-by-step explanation:

The annual consumption (in billions of units) is described by the exponential function ...

f(t) = 45.5·1.026^t

The accumulated consumption is described by the integral ...

$\displaystyle\int_0^t{f(x)}\,dx=45.5\int_0^t{1.026^x}\,dx=45.5\left(\dfrac{1.026^t-1}{\ln{1.026}}\right)$

We want to find t such that the value of this integral is 2625, the estimated oil reserves.

2625 = 45.5/ln(1.026)·(1.026^t -1)

2625·ln(1.026)/45.5 +1 = 1.026^t ≈ 1.480832 +1 = 1.026^t

Taking natural logs, we have ...

ln(2.480832) = t·ln(1.026)

t ≈ ln(2.480832)/ln(1.026) ≈ 35.398

After about 35.4 years, the oil reserves will run out.

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