Shown to the right is a certain population for selected years between 1950 and 2

Question

Shown to the right is a certain population for selected years between 1950 and 2005. Use the table to answer questions a) through e). a) Use regression to fit a logistic equation N(t) = c/1 + ae^-bt to the data. N(t) = (Type an exact answer in terms of e. Use integers or decimals for any numbers in the equation. Round to three decimal places as needed.) b) Estimate the limiting value of the function. What number will the population approach in the long run? The population will approach people. (Type an integer or decimal rounded to the nearest whole number as needed.) c) Graph the function. Choose the correct graph below. Each viewing window is [-2, 70, 7] by [-2400, 26000, 2600].

Explanation / Answer

Using solver in excell to minimize sum of squares, following values of a,b,c are obtained

(b) Limiting value is when t tends to infinity

N(t) = c/1+0 = c =23021

c a b 23021.48 14.8156967 0.102934 year after 1950 population N(t) error sq of error t p(t) e(t) = N(t)-p(t) e^2 0 1057 1455.61 398.6095266 158889.555 20 8143 7963.694 -179.3059945 32150.6397 30 13885 13740.28 -144.7232028 20944.8054 40 18064 18546.15 482.1517681 232470.327 50 21578 21194.41 -383.5885517 147140.177 55 21801 21893.43 92.429422 8543.19805 sum of squares 600138.702

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