Two parts: 47. How to find equation for semi log plot? (How did they get 9.127 i

Question

Two parts: 47. How to find equation for semi log plot? (How did they get 9.127 in the answer key?) 48. (Similar question as 47)
Answer to 47. 1.7 Sequences and Difference Equations 85 on the same plot. From this line, provide an estimate of the average growth rate exponentr for the pop- ulation size function x(t) = ce" over this period of 750 years 48. Consider the entri es presented in the table below which represent one estimate of the world's popula- tion levels over the period 1920 to 2010: Population size x (in billions) 1.86 2.07 2.30 2.52 3.02 3.70 4.44 5.27 5.98 6.86 7. Consider the entries presented in the table below Year AD (t) which represent one estimate of the world's popula- tion levels over the period 1750 to 1920: 1920 1930 1940 1950 1960 1970 1980 1990 1999 2010 Population Year AD () size r (in billions) 1750 1800 1850 1900 1910 1920 0.79 0.98 1.26 1.65 1.75 1.86 Provide a semi-log plot of the points (t, In x) and find and graph the best-fitting line through these points on the same plot. From this line, provide an estimate of the average growth rate exponentr for the pop- ulation size function x(t) = ce" over this 170-year period Provide a semi-log plot of the points (t, In x) and find and graph the best-fitting line through these points on the same plot. From this line, provide an estimate of the average growth rate exponent r for the pop- ulation size functionx(t)-ce" over this 90-year period.

Explanation / Answer

To write the equation from the given graph, it is seen that graph reprsents a line of the form Y= mt +b, where Y is the logarthmic axis and t is thw linear axis in this semi -log graph. From the graph we have to find out the slope and Y intercept.   Y intercept from the graph readable is -0.16 on the logarthmic axis. This would when converted would give 9.127

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