The diameter of a bacteria colony that doubles every hour is represented by the graph below. what is the diameter of the bacteria after 10 hours?
graph of a curve passing through the points zero comma 1, one comma two, two comma four, and three comma eight

Do you notice anything strange about those points ?

(0, 1), 
(1, 2), 
(2, 4),
(3, 8).

The y-coordinate of each point is (2) raised to the  power of the x-coordinate.

First point:       x=0,  y=2⁰ = 1
Second point: x=1,  y=2¹ = 2
Third point:      x=2,  y=2² = 4
Fourth point:    x=3,  y=2³ = 8

The equation of the curve appears to be

                               y = 2 ^ x .

So, after 10 hours,  x=10, and  y = 2¹⁰ = 1,024 .