Question

11. Aviation The number of active certified commercialpilots has been declining since 1980, as shown inthe table.a. Find a linear equation that can be used as a modelto predict the number of active certified commercialpilots for any year. Assume a steady rate of decline.

Answer 1

a. The line equation is given by:

`y=mx+b`

Where m is the slope of the line and b is the y intercep.

In this case y is the number of active pilots and x is the year.

In order to obtain the line equation of the function, you use the information about a pair of years in the given table, in order to calculate the slope of the line. You can select whichever two years with its number of active pilots.

For example, for years 1980 and 1990, you have that the pilots were 182,097 and 149,666 respectively.

To calculate the slope of the line, you use the following formula:

`m=(149,666-182,097)/(1990-1980)=-3,243.1`

Then, the slope of the line is negative.

If you consider the zero point of the year axis, as the year 1980, the y intercept of the function will the value of the active pilots in that years, which is 182,097.

Finally, the line equation is:

`y=-3,243.1x+182,097`

b. For the year 2003, you have that x is:

x = 2003 - 1980 =23

You replace this value of x into the linear equation:

`y=-3,243.1(23)+182,097=107506`

The number of active pilots for 2003 is 107,506