A country has 155 years of oil reserves at the current rate of consumption. Suppose that the demand for oil in the country is 2,000,000 barrels per year. Furthermore the oil is consumed at a rate that increases 2% per year. a. How much oil will be used at the end of 42 years? b. How long will the oil reserves last?

a) 125,220,046 barrelsb) 71.25 years

Step-by-step explanation:

Oil consumption:

2000000 barrels/year

Rate of increase of consumption:

2% = 0.02 per year

Total reserves

155*2000000 = 310000000 barrels

a)

Total oil consumption at the end of 42 years:

2,000,0002,000,000*1.02 = 2.000,000*1.02^2...2,000,000*1.02^41

Sum:

2000000*(1 + 1.02+ 1.02^2+ ...+ 1.02^41) = 2000000*(1.02^41 - 1)/(1.02 - 1) = 125,220,046 barrels

b)  

Oil reserves will last:

2000000*(1.02^x - 1)/(1.02 - 1) = 310000000(1.02^x - 1)/0.02 = 1551.02^x - 1 = 155*0.021.02^x =1 +3.11.02^x = 4.1x log 1.02 = log 4.1x = log 4.1 /log 1.02x =  71.25 years

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