Problem

If the points

all lie on a curve of the form

what are the values of a and C?

Solution

First we note that we are not discussing a "best-fit" curve, so we should be able to take a value of x, plug it into the function, and get the corresponding value of y from the table.

Since there are 4 points in the table, we have enough information to find a and c.

When x = 0, y = 2. Therefore,

Simplify to get c = 2, so we're halfway done.

When x = 1, y = 5, so plug these values into the function:

Simplify to get a = 3. Thus the equation is

We may test that this is correct by checking other values from the table.

So the solution checks out.