Question

An insect population after `x` months can be modeled by the graph. See the table below and write the exponential function that describes this scenario.

months, x, to population, y

0 to 12
1 to 18
2 to 27
3 to 40.5

Answer 1

Use the form y = a·b^x. Here a = y(0) = 12 and b = 18/12 = 1.5, so the exponential model is

y = 12(1.5)^x.

(Equivalently y = 12·e^{x ln 1.5}.)