find exponential function

Question

Write an exponential function in the form y, equals, a, b, to the power x y=abx that goes through the points left bracket, 0, comma, 9, right bracket(0,9) and left bracket, 2, comma, 225, right bracket(2,225).

Answer 1

Each of the points (0, 9) and (2, 235) is a point (x, y) and so for x = 0, y would equal 9 and for x = 2, y would equal 225.

If y = ab^x then plugging in the point (0, 9) we would have:

9 = ab⁰ and since a constant (b) raised to the zero power = 1, then a = 9

Now that we know a = 9, we can say y = 9•b^x and then plugging in x = 2 and y = 225 we get:

225 = 9•b²

225/9 = b²

25 = b²

b = 5

Therefore y = 9•5^x is the exponential function