Please post step by step.
You already have loads of step-by-step solutions in your textbook, in your class notes, and on the various websites you've reviewed. So one more fully-worked solution isn't likely to make much difference. It's time now to
do, rather than just
watching again. So:
In 2008, there was an average of 313 high school students per guidance counselor. The average number of students per counselor is decreasing about 27.2 students per counselor each year. Let a. be the average number of students per guidance counselor at t years since 2008.
A. Find an equation of a linear model is a =
B. The predicted average number of students per counselor in 2015 is =
C. The ratio will be reached in the year =
"At t years since 2008" means that "Year zero" is 2008. Then t = 1 for 2009, t = 2 for 2010, and so forth.
A. You are given one data point, at t = 0. What is the value of "a" when t equals zero?
You are also given a rate of growth (well, decline, but the process is the same). What is this rate of year-on-year change? (Don't forget the sign!) So, in 2009, what must have been the value of "a"?
This gives you a second data point, at t = 1. If you're not already sure of what the slope m is for this exercise, plug this and the given data point into
the formula for slope to find the value for m.
Now that you have a point (given) and a slope (given, or computed), you can find the equation for the line, using any of
methods commonly used. (You'll be using t instead of x and a instead of y, but the process is the same.)
What then is your linear "model"?
B. What is the value of t when the year is 2015? Plug this into your model.
C. This part appears to be missing some necessary information. What is the target ratio that you're supposed to be testing against?
When you reply, please include your efforts so far, including your answers to the leading questions asked above. Thank you!