Question 138990
Look at the way the value of f(x) changes with each change in x.

In table 1, each time x increases by 1, f(x) increases by a factor of 3. That is, each subsequent value for f(x) is 3 times greater than the previous value.

Since f(0) = 4, let's guess that {{{f(x) = 4 * 3^x}}} 
Now test that guess using other value of x. {{{f(1) = 4*3}}} = 12. check. do some others to prove out the guess.


In table 2, each time x increases by 1, f(x) decreases by the quantity (0.5) . That is, each subsequent value for f(x) is 1/2 less than the previous value. 

That is a line with a slope of -(1/2). The value of f(0)= 3. Which is the y intercept. So let's guess the line is {{{f(x) = (-1/2)x + 3 }}} 

test that out using a few values for x and see how it goes.