The table shows per capita peach consumption.t Per Capita Consumption of Peaches

Question

The table shows per capita peach consumption.t Per Capita Consumption of Peaches (pounds) Price (above $1.50 per pound) 0.00 0.10 0.20 0.30 0.40 0.50 4.7 4.74.6 6.0 7.0 6.9 6.9 6.8 7.4 15.0 49 2 6.4 6.3 62 .1 7.5 81 8080 3 7.2 47.8 5 8.2 6 8.6 7.4 7.9 8.3 7.7 7.6 85 8.4 83 8.2 (a) Find the function of the logarithmic cross sectional model that gives per capita consumption of peaches at a price of?1.50 per pound, where r represents yearly family income in tens of thousands of dollars, with data from 1sfs6. (Round all numerical values to three decimal places.) 0.00,1.179(1.511)xb (b) Calculate per capita peach consumption for families with a yearly income of $55,000 when the price is $1.50 per pound. (Round your answer to one decimal place.) lb

Explanation / Answer

A) To find the function of the logarithmic cross-sectional model that gives per capita consumption of peaches at a price of $1.50 per pound, where f represents yearly family income in tens of thousands of dollars, with data from 1<=f<=6 is found by modelling the column with price(p) $1.50 of data in the table

c(0.00,f) = a + b ln(f) - Basic logrithmic cross sectional function

5 = a + b*ln(10000) = a + b*9.2103

6.4 = a + b*ln(20000) = a + b*9.9034

Solving the above to equation for 2 variables we get

a = -13.6 & b = 2.019

c(0.00,f) = -13.6 + 2.019*ln(f)

Function of the logarithmic cross-sectional model that gives per capita consumption of peaches at a price of $1.50 per pound? is c(0.00,f) = -13.6 + 2.019*ln(f)

b) f = $55000

c(0.00,f) = -13.6 + 2.019*ln(f)

=-13.6 + 2.019*ln(55000) = -13.6 + 2.019*10.91 = 8.4432

Per capita peach consumption for families with a yearly income of $ 55,000 when the price is $1.50 is 8.44

Family income, f Per capita consumption, c $10,000 5.0 $20,000 6.4 $30,000 7.2 $40,000 7.8 $50,000 8.2 $60,000 8.6

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