Question

In the year 2000 (t=0), the world reserves of natural gas were approximately 6112 trillion cubic feet. In that same year, the world consumption of natural gas was approximately 99.6 trillion cubic feet, and was growing exponentially at about 3.1% per year. If the demand continues to grow at this rate, and no new reserves of natural gas are found, in what year will the world reserves of this resource be depleted? . The world reserves will be depleted in the year (Round to the nearest year as needed.)

Answer 1

Formulating the given data,

Total reserves-Total consumption at the growth rate,g=3.1%p.a. .for "n" no. of yrs.= 0,

(Using compound interest fromula, for growth in consumption)

ie.6112-(99.6*(1+0.031)^n)=0

Solving for n, we get

the no.of yrs. = 134.849

so, the reserves will get depleted in the 135 th year from t=0, 2000

ie. Year 2135

The world reserves will be depleted in the Year 2135