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 28
3 to 41

Answer 1

An exponential model is y = ab^x. From x = 0 we have a = 12. Using x = 3, y = 41 gives 12·b^3 = 41, so b = (41/12)^(1/3).

Thus an exact form is
y = 12·(41/12)^(x/3).

Decimal form (rounded) is
y ≈ 12(1.507)^x.