The total sales of a company in 2008 were $45,000. In 2011, it grew to $84,000. Use
� as the number of years since 2000 and � as the total sales, and answer the
following:
a. What is the rate of change (slope) in the total sales?
b. Write an equation in both point-slope form and slope-intercept form modeling
the company’s sales.
c. What are the projected sales for the year 2016? (16 years after 2000.)
The above answer is wrong. (84000-45000) is not 28000, it is 39,000. Therefore 39000/3 is 13000. M =13000.
There are two points:
(8,45000) and (11,84000)
a, the rate of change is (84000-45000)/(11-8) = 28000/3
b, use the slope 28000/3 and a point, you can plug into the formulas
c, once you have the equation, plug in 16 then you will get the answer
a. To find the rate of change (slope) in total sales, we can use the formula for slope:
slope = (change in y) / (change in x),
where x represents the number of years since 2000 and y represents the total sales.
In this case, the change in y is the difference between the sales in 2011 ($84,000) and the sales in 2008 ($45,000), which is $84,000 - $45,000 = $39,000.
The change in x is the difference in the number of years since 2000 between 2011 and 2008, which is 2011 - 2008 = 3 years.
Therefore, the slope is:
slope = (change in y) / (change in x) = $39,000 / 3 = $13,000 per year.
b. To write an equation in point-slope form, we'll use the point (x1, y1) = (0, $45,000) (since it represents the sales in 2008) and the slope we found in part a, which is $13,000 per year:
y - y1 = m(x - x1),
where m is the slope. Plugging in the values we have:
y - $45,000 = $13,000(x - 0).
Simplifying,
y - $45,000 = $13,000x.
To write the equation in slope-intercept form, we'll continue simplifying:
y = $13,000x + $45,000.
c. To find the projected sales for the year 2016 (16 years after 2000), we'll substitute x = 16 into the equation we found in part b:
y = $13,000x + $45,000.
y = $13,000(16) + $45,000.
Calculating,
y = $208,000 + $45,000.
y = $253,000.
Therefore, the projected sales for the year 2016 is $253,000.