Question

An insect population after x months can be modeled by the graph at left. Complete the table below and write the exponential function that describes this scenario.
months, x: 0, 1, 2, 3
Population, y: 12, 18, 27, 41

Answer 1

The population multiplies by a constant factor each month: 18/12 = 27/18 = 1.5. So the model is exponential with initial value 12 and base 1.5.

Completed table (exact values):
- x = 0 → y = 12
- x = 1 → y = 18
- x = 2 → y = 27
- x = 3 → y = 12(1.5)^3 = 40.5 (rounded to 41 insects on the graph)

Exponential function:
y = 12(1.5)^x (or y = 12(3/2)^x).