World production of copper, in millions of tons per year, from 1900 to 2000 is g

Question

World production of copper, in millions of tons per year, from 1900 to 2000 is given by

C = 0.5 1.033t,

where t is the time in years since 1900.†

(a) What production level (in millions of tons) does this model give for the year 2000? (Round your answer to two decimal places.) million tons

(b) If this model were extended to 2029, how could you use your knowledge of copper production in 2028 to estimate copper production in 2029? To estimate copper production in 2029 we would multiply copper production in 2028 by .

Explanation / Answer

(a) C = 0.5X1.033t

In year 2000, t=100 (from year 1900)

Hence production level is given by :

C = 0.5 X 1.033 (100) = 51.65 millions of tons in 2000

(b) if this is extended to 2029, then for year 2028, t=128

Hence C = 0.5X1.033(128) in year 2028

=> C = 66.112

Now we multiply this by 1.0078125 to get copper production in 2029

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