1. The population of a city is shown below in a graph plotted vs. year in linear

Question

1. The population of a city is shown below in a graph plotted vs. year in linear & log scales.

(a) The gain is defined as Gain = 10 Log[x/200,000], how many dB/decade is the population of this city growing?

(b) What's the best way to model the population growth in this city? Model is as an exponential function or as a power function? Explain.

Population history: 250 200 (from Apr 1990 to 2016) (in thousands of people) 150 1995 2000 2005 2010 2015 Population history: 300 250 200 (from Apr 1990 to 2016) (in thousands of people) (log scale) 150 100 995 2000 2005 2010 2015

Explanation / Answer

a). gain at 2000yr = 10log(140000/200000) = -1.55dB

gain at 2010 yr = 10log(210000/200000) = 0.21dB

So dB/Decade = 0.21dB + 1.55dB = 1.76dB/Decade.

b).As the slope of linear scale and log scale looks the same, So the best model to describe the population function is power function(power of 10).

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