This is a pretty basic related rates problem. I'm going to go through this just like I do in class when I'm teaching it to my students.
We see we have a snowball, which is a sphere. We are talking about the surface area of this sphere which has a formula of
In the problem we are given diameter, not radius. What we know about the relationship between a radius and a diameter is that
d = 2r so
Now we can have the equation in terms of diameter instead of radius. Rewriting:
which simplifies to
and a bit more to
(the 4's cancel out by division). Now that is a simple equation for which we have to find the derivative with respect to time.
Now let's look at the problem and see what we are given as far as information.
The rate at which the surface area changes is -3.8, and we are looking for , the rate at which the diameter is changing, when the diameter is 13. Filling in:
and solving for the rate at which the diameter is changing:
and divide to get
Obviously, the negative means that the diameter is decreasing.
system of equations means that we have a given number of equations with the same solutions.
If you only have tables, this means that you need to have one table for each equation:
For example, if you are working only with two variables, x and y, in those tables you can see the pints (x, y) that belong to each equation.
Now, a point (x, y) will be a solution of the system of equations only if it belongs to the data table for each equation
This would mean that if you graph those data sets, the graphs will intersect at the point (x, y) that belongs to all the tables of data.
another way may be using the data in the tables to construct the equations, but you said that you only want to use the tables, so this method can be discarded.