The annual growth rate of energy utilization in the world was 3.5% per year in t

Question

The annual growth rate of energy utilization in the world was 3.5% per year in the period from 1950 to 1973. How long would it take to consume all available resources if the consumption growth rate of 3.5% per year is maintained?

a. Assume that the global energy resources available at the moment are sufficient to sustain the world for 1000 years at the current utilization rate.

b. Assume that the global energy resources at the moment are sufficient to sustain the world for 10,000 years at the current utilization rate.

Explanation / Answer

From the given question.

the growth is in geometric progression with common ratio 1.035

a) sum of n terms of a GP is given by

Sn= a(rn-1)/(r-1)

1000= 1(1.035n-1)/(1.035-1)

1.035n-1=35

1.035n=36

n= log36/log1.035

n=104.16

It will take 105 years.

b. 10000= 1(1.035n-1)/(1.035-1)

1.035n-1=350

1.035n=351

n= log351/log1.035

n=170.36

It will take 171 years.

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