How many years the world's oil reserves will be enough? 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.
