Basically, when dealing with exponential functions, they have the general form:
y = ab^x, where a = initial value and b = base or growth factor.
If b > 1, then the function is exponential growth. If 0 < b < 1, meaning if b is between 0 and 1, then the function is exponential decay. Also, b = 1 + r, where r = the percent rate of change.
In this particular case, we have the set of table values for 3a). To find out if the function is exponential, simply take the f(x) values and divide the values like so:
43.5/87 = 0.5
87/174 = 0.5
The fact that both divisions equal 0.5 indicates an exponential function.
Using the formula for exponential functions, y = ab^x, we first find a. Since x = 0 and 6 y = f(x) = 43.5, 43.5 = a, the initial value.
Now, we must find b. To find b, plug in a given point along with a into the formula, then solve for b as follows:
y = ab^x
87 = 43.5b^1
87/43.5 = b
2 = b
So, now that we've found a and b, we can now write our exponential formula:
y = 43.5(2)^x
3b) is just a linear equation. I'm sure you can figure that one out yourself.