The world population at the beginning of 1990 was 5.3 billion. Assume that the p

Question

The world population at the beginning of 1990 was 5.3 billion. Assume that the population continues to grow at the rate of approximately 2%/year and find the function Q(t) that expresses the world population (in billions) as a function of time t (in years), with t = 0 corresponding to the beginning of 1990. (Round your answers to two decimal places.)

(a) If the world population continues to grow at approximately 2%/year, find the length of time t0 required for the population to double in size.
t0 = ( )yr

(b) Using the time t0 found in part (a), what would be the world population if the growth rate were reduced to 1.8%/yr?
( ) billion people

Explanation / Answer

(a) Q(t) = 5.3 x (1.02)^t

we require when 1.02^t = 4

=> tln1.02 = ln4

i.e. t = ln4/ln1.02 = 70.01 years

(b) Q(70.01) = 5.3 x (1.016)^70.01 = 16.10 billion

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