Question

What equation best models this data? (Use y to represent the population in millions, and t to represent the year, assuming that 2010 is t = 0.)

Answer 1

Answer:

y = 2.31x + 309.35

Step-by-step explanation:

Whenever you are checking for a best fitting equation you want to check if it has a constant slope.  If it does then the relation is linear and super easy.

So, since the t values are increasing by the same amount you want to see if the y values are  too.  And they are, each population entry is increasing by 2.31, this is the slope.  

Also, keep in mind you can caluclate slope with the equation $\frac{y_2-y_1}{x_2-x_1}$  here x is replaced by t though.

Now, since we know it's linear and we know the slope we can find the equation with the formula  y - y1 = m(x - x1) where again, x is replaced by t and m is the slope 2.31

I am just going to use the first point.  so x1 = t1 = 0

y - 309.35 = 2.31(x-0)

y = 2.31x + 309.35

Let me know if there was something you didn't understand.