Question

Find the equation of the exponential function represented by the table below

x y
0 3

1 9

2 27

3 81

Answer 1

y = 3^(1 + x)

Explanation:

Notice that each time x increases by 1, y increases by a factor of 3.

Thus, the required equation has the form y = 3^x.

Check: If x = 0, do we get 3? No. Therefore we must modify the exponent:

y = 3^(1 + x)

Check: If x = 0, do we get 3? 3^(1 + 0) = 3 (correct)

If x = 2, do we get 27? 3(1 + 2) = 3^3 + 27 (correct)