ANSWER:
i) y = 25x + 500
ii) y = 30x + 400
iii) The washing machines would cost the same amount after 20 years of use
iv) Standard machine
Step-by-step explanation:
i)
We are to determine a straight line equation that models the cost of High-Efficiency washing machine over the years;
The first step step is to determine the slope of the line,
( change in y) / ( change in x ) = (550 - 525) / ( 2 - 1) = 25
The equation is slope-intercept form will be;
y = 25x + c
Where y is the cost of the High-Efficiency washing machine and x the number of years. To determine the y-intercept, c, we use any pair of points given in the data table;
when x = 1, y = 525
525 = 25(1) + c
c = 500
Therefore;
y = 25x + 500
ii)
The straight line equation that models the cost of Standard washing machine over the years;
Slope = (460 - 430) / (2 - 1) = 30
The equation is slope-intercept form will be;
y = 30x + c
when x = 1, y = 430
430 = 30(1) + c
c = 400
Therefore;
y = 30x + 400
Where y is the cost of the standard washing machine and x the number of years.
iii)
Given the cost functions for both machines over the number of years, we simply equate the two equations and determine the value of x when both machines would cost the same amount;
We have the cost functions;
y = 25x + 500
y = 30x + 400
Equating the two and solving for x;
25x + 500 = 30x + 400
500 - 400 = 30x - 25x
100 = 5x
x = 20
Therefore, the washing machines would cost the same amount after 20 years of use.
iv)
In order to determine which machine would be the more practical purchase if kept for 9 years we use the cost functions obtained in i) and ii)
The cost function of the High-Efficiency washing machine is;
y = 25x + 500
To determine the cost, we solve for y given x = 9
y = 25(9) + 500
y = 725
The cost function of the Standard washing machine is;
y = 30x + 400
We solve for y given x = 9
y = 30(9) + 400
y = 670
Comparing the two values obtained, the cost for the Standard washing machine is more practical.
