World oil reserves are estimated at around 240 billion tonnes. Its world production is 4.36 billion tons annually. Calculate how many years the world's oil reserves will be enough: a) if the current level of its production is maintained; b) taking into account the growth of extraction by 2% per year. My try is:
a) $\frac{240}{4.36}≈55.05$ enough for 55 years.
b) $4.36+4.36\cdot 1.02+4.36\cdot (1.02)^2+⋯+4.36*(1.02)^n=4.36\cdot \frac{1\cdot(1.02^n-1)}{1.02-1}=4.36\cdot \frac{1.02^n-1}{0.02} =218\cdot(1.02^n-1)>240$
$$1.02^n-1 >\frac{240}{218}$$ $$1.02^n>2.101$$ $$n > \frac{\ln (2.101)}{\ln(1.02)} ≈ 37.5$$ enough for 37 years.
But the answer in test is a)55 and b)26. Can you help please.
I used Excel to calculate this, and found that after 37 years, 235 B will be extracted, so it appears your calculation is correct. And doing a rough estimate, we can use an approximation 2%*26*e = 141%, so in 26 years, production should be about 41% higher than today. But 26 is about half of 55, which would mean that production would have to be, on average, about twice current levels. So even without a calculator, 26 is clearly wrong.
As far as speculating as to where 26 came from, if you divide the current reserves by the current rate plus the reserves times 2%, you get 240/(4.36+240*.02) = 26.2, which rounds to 26. So this could be a coincidence, or perhaps your teacher did something along those lines.