Question

Based on actual and projected data from 1995 to \(2000,\) a linear model for a company's profit \(P\) is \(P=3,005,000-900 t,\) where \(t\) represents the number of years since 1995. Sketch two graphs of the model. In the first graph, divide the vertical axis into \(\$ 1,000,000\) intervals. In the second graph start at \(\$ 3,000,000\) and use \(\$ 1000\) intervals.

Short answer

Two graphs were created from the linear profit model of a company. The first graph showed the general trend of the company's profit from 1995, with the vertical axis divided in $1,000,000 intervals. The second graph offered a more detailed view, starting from $3,000,000 and using $1,000 intervals.

Step-by-step solution

Prepare for Graph 1

Get a graph paper and mark the vertical axis values in increments of $1,000,000. Remember, the horizontal axis represents the time 't' in years since 1995, so denote accordingly.

Plot the Linear Model for Graph 1

Using the given linear model equation \(P=3,005,000-900t\), substitute different values of 't' to generate points on the graph. Start by substituting \(t = 0\) (1995), then increase in one year intervals. Connect the points to form a straight line representing the company's profit trend.

Prepare for Graph 2

For the second graph, again get a graph paper, but this time start the vertical axis at $3,000,000 and mark increments in $1,000 intervals up to ideally, at least, the highest profit.

Plot the Linear Model for Graph 2

With the same linear model equation \(P=3,005,000-900t\), substitute different values of 't' again to generate the points on the graph. Note that due to the smaller intervals this graph will provide a more detailed view of the change in profit over time.