|
Question 843033: Please HELP ME: The American Association of Fund Raising Counsel keeps track of the total number of charitable donations to all the different charities in the US. Let C represent the total amount of donations(in billions of dollars) in the year that is: t years since 2000. Then a reasonable linear model for C is: C=17t + 209. a) state the slope of this model and then write a sentence to explain what it means in the context of the situation. b) state the coordinates of the t-intercept. Then write a sentence to explain what it means in the context of the situation.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! The formula is C = 17T + 209.
When T = 0, the year is 2000.
That is the y-intercept and, if you solve the formula for T = 0, you will see that C = 209 which means that contributions in the year 2000 were equal to 209 billion.
The formula is the equation of a straight line in y-intercept form.
y-inercept form of the equation of a straight line is:
y = mx + b
m is the slope and b is the y-intercept.
The slope of your equation is 17 and the y-inercept is 209.
The y-intercept was discussed above.
It's the value of C when T is equal to 0.
The slope indicates the number of billions of dollars that the contributions are increasing each year.
If you show the formula for the first 3 years, that give you an indication of what is going on.
The formula is C = 17T + 209
When T = 0, the formula says that C = 0*17 + 209 = 209
When T = 1, the formula says that C = 1*17 + 209 = 209 + 17 = 226
When T = 2, the formula says that C = 2*17 + 209 = 209 + 34 = 243
look at the increase per year and you will see that it is equal to 17 each year.
The formula is telling you that the number of contributions are equal to 17 billion * the number of years from the year 2000 plus 209 billion.
When T = 0, the year is 2000
When T = 1, the year is 2001
When T = 2, the year is 2002
etc.
|
|
|
| |
