Question

Use the table to calculate the average rate of change from t=1 to t=4.

t= 0, 1, 2, 3,4
x(t)= 8, 7,5,1,2

I don't know how to make a table. HELP PLEASE.

Answer 1

Hi @izhangy, technically you have your table already, because it is nothing more than a list of one variable (t) versus another variable, here x(t).

The rate of change is defined as (x(t+1)-x(t)) / (t+1 - t). Looks impressive but is nothing more than a fancy way of telling you that you need to subract to successive x-values and divide this by two successive t-values.

Let's start with the t-part. As you can see, t neatly increases with '1' for each step, going from 0 to 1 to...etc to 4. Every step is therefore of size '1' and that makes life easy.

Now the x(t)-part. Just start with the first one, 8. The next value is 7, so the difference is 8-7=-1. In our formula above, this means that x(1) - x(0) = 8 - 7 = -1. The rate of change for this step is then: -1 / 1 = -1.

Let's do the second one as an example too. Now we evaluate t=1, so we need x(t+1)=x(2), x(t)=x(1) and this goes together with t=2 and t=1. Just fill out the formula and find as rate of change for the second step: ( x(2)-x(1) ) / 2-1 = 5-7/1 = -2. The rate of change has increased from -1 to -2 by stepping from t=0 to t=1. Can you do the rest ?