Gasoline prices for the first six months of 2004 are shown in the table below. using a logarithmic model, what is the best prediction for gas prices in the ninth month of 2004? average monthly gas prices in 2004 month average price 1 1.592 2 1.672 3 1.766 4 1.833 5 2.009 6 2.041 a.$2.10 b.$2.16 c.$2.32 d.$2.42

Option: c is the correct answer.

c.   $ 2.32

Step-by-step explanation:

We are given a table of values as:

Number of months              Monthly gas price(in $)

             1                                   1.592

             2                                  1.672

             3                                  1.766

             4                                  1.833

             5                                  2.009

             6                                  2.041

On plotting these points in a regression graph we obtain the line of best fit as:

Now we are asked to find the gas price in the ninth month.

i.e. we have to find the value of y when x=9.

Hence,

Hence, option c is the correct answer.

c. y = 1/4 x + 5

step-by-step explanation:

first, put the equation of the line on the graph into slope-intercept form

(y = mx + b):   y = -4x + 8

second, a perpendicular line has to have "an opposite/reciprocal slope" to the original slope. so, find the "m" value in your original equation (it's -4, right? )

original slope: m = -4   perpendicular slope: change the sign to its opposite and find the reciprocal ("flip" the number)

new slope is now positive (b/c the original slope was negative 4), and it's 1/4 (not the original slope of 4 or 4/1)