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.
in the given closed interval, so the area is exactly given by the definite integral
