Question

Use the graph to answer the question.

"Graph: An exponential curve on a coordinate plane from x-axis negative 5 to 5 and y-axis 0 to 10, passing through (0, 1) and (1, 0.5), approaching x-axis."

Write the exponential equation shown in the graph. If it passes through 0,1 and 1,0.5

Answer 1

Use y = a·b^x. Plugging (0,1) gives a·b^0 = a = 1.
Plugging (1,0.5) gives 1·b = 0.5, so b = 0.5.

Thus the equation is y = (0.5)^x, equivalently y = (1/2)^x (or y = 2^{-x}).