Any times you see the phrase: "Rate of Change", or even sometimes just the word "Rate" think slope.
The word slope is just a fancy word that means the rate of change.
Rate of Change is just a fancy phrase meaning how much does something change over some amount of time. So in this case our rate of change will have the units of inches per year.
Let's get to the problem at hand! We'll need to find slope / the rate of change (the two are interchangeable with each other). Let's go over the formula for slope:
m = (y2 - y1) / (x2 - x1)
First we will need to label each of the "coordinated points (the two numbers that go together in a pair)" with either (x1,y1) or (x2,y2).
A Giant Red Oak's diameter in 1965 was 248 inches. Keep in mind time is ALWAYS going to be X in rate of change problems (and most all problems for that matter).
(1965,248) (X1,Y2)
(2005,251) (X2,Y2)
Plug in the values into the equation! m = (y2 - y1) / (x2 - x1) m = (251 - 248) / (2005 - 1965) m = (3) / (40)
Type that into a calculator to get a decimal value over 1. m = 0.075 inches per 1 year. Or...
Every kilogram is 1,000 grams, but you want 10 kilograms. You can multiply 1,000 10 times (you can also add 1,000 10 times,) giving you the answer > 10,000.
We have 11 as our base value, meaning that we add 11 to something, so we have 11+<something>. To find that something, we want to know how long it takes to go 21.78 miles at 33 miles per hour. To get this, we want to turn miles per hour into minutes per mile and multiply that by 21.78 miles to get our answer. Therefore, we cross them out as shown in the equation to get
