in 1994, the profit is $250,000
in 1995, the profit is $280,000
in 1996, the profit is $240,000
in 1997, the profit is $320,000
in 1998, the profit is $310,000
this information is in a chart but charts don't work here so anyways
[it looks something like this:
Year: 1994 1995
Profit: $250,000 $280,000
etc]
so I have to make a scatter plot of the data, which is pretty easy and answer a few questions.. here are the questions that I didn't get:
1. Write a linear model for the amount of profit.
2. Write a linear model to estimate the profit in 2002.
please show/explain how to do these. thnk u
I answered this below, rather wordily. If there's something else I can explain, do ask.
To write a linear model for the amount of profit, we need to find the equation for a straight line that fits the given profit data points. The equation for a straight line can be written as y = mx + b, where y represents the dependent variable (profit), x represents the independent variable (year), m represents the slope of the line, and b represents the y-intercept (the value of y when x is 0).
To find the slope, m, we need to calculate the change in profit divided by the change in year. Let's take two data points: (1994, 250,000) and (1998, 310,000).
Change in profit = 310,000 - 250,000 = 60,000
Change in year = 1998 - 1994 = 4
Slope (m) = Change in profit / Change in year = 60,000 / 4 = 15,000
Now let's use the point-slope form of the linear equation, using one of the data points. We can choose (1994, 250,000) and substitute the values into the equation.
y - y1 = m(x - x1)
y - 250,000 = 15,000(x - 1994)
Simplifying further,
y - 250,000 = 15,000x - 29,910,000
y = 15,000x - 29,910,000 + 250,000
y = 15,000x - 29,660,000
This equation represents the linear model for the amount of profit.
For the second question, we need to estimate the profit in 2002 using the linear model.
To do this, we substitute the year 2002 into the linear model equation we derived earlier.
Profit (2002) = 15,000(2002) - 29,660,000
Profit (2002) = 30,030,000 - 29,660,000
Profit (2002) = $370,000
Therefore, the estimated profit in 2002 is $370,000.