Given that the gallon of oil cost $4 and that of diesel costs $5.24, to get the time taken for the gallon of oil to cost more than that of diesel we shall proceed as follows;

Using the compound interest formula;

A=p(1+r/100)^n

where;

A=future amount

p=initial amount

r=rate and n=time;

thus substituting our values in the expression we have:

5.24=4(1+10/100)^n

5.24/4=(1.1)^n

introducing the natural logs we get:

ln(5.24/4)=nln1.1

thus;

n=(ln 1.31)/(ln 1.1)

n=2.8

Therefore is will take 2.8 years for oil to cost more than diesel per gallon.

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