#23 On October 17, 2006. in an article called \"US Population Reaches 300 Millio
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Question
#23
On October 17, 2006. in an article called "US Population Reaches 300 Million, " the BBC reported that the US gains 1 person every 11 seconds. If f(t) is the US population in millions t years after October 17, 2006, find f(0) and f'(0). The following table shows the number of hours worked in a week, f(t), hourly earnings, g(t), in dollars and weekly earnings, h(t), in dollars, of production workers as functions of t, the year.^6 (a) Indicate whether each of the following derivatives is positive, negative, or zero: f'(t), g'(t), h'(t). Interpret each answer in terms of hours or earnings. (b) Estimate each of the following derivatives, and interpret your answers: (i) f'(1970) and f'(1995) (ii) g'(1970) and g'(1995) (iii) h'(1970) and h'(1995)Explanation / Answer
Given that rate of change of population = 11 times Population
Let f(t) be the population at time t.
Then f'(t) = 11 f(t)
Separate the variables
f'(t)/f(t) = 11 dt
Integrate
log f(t) = 11t +C
Or f(t) = Be11t
When t=0 it was Oct 2006
f(0) = 300 million
Hence B = 300 million
Or f(t) = 300 e11t where t is in seconds
f'(t) = 3300e11t
f'(0) = 3300
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