Question

You have an ant farm with 31 ants. The population of ants in your farm will double every 3 months. The table shows the population growth of the ants over nine months. Decide whether the table represents a linear function or a nonlinear function. After one​ year, how many ants will there be in the ant​ farm?

Answer 1

I think the table is linear. The total amount after one year is 248 ants.

Step-by-step explanation:

Answer 2

The ant farm population exhibits exponential growth, which is a nonlinear function, and after one year, there will be 496 ants.

Step-by-step explanation:

The scenario described in the question exhibits an example of exponential growth, where the population of ants doubles at regular time intervals. This type of growth results in a population size that increases at an accelerating rate over time, which is a characteristic of a nonlinear function. Since we are told that the ant population doubles every 3 months, we can calculate the population after one year, which consists of four 3-month intervals.

Starting with 31 ants, after three months (1 interval), there will be 31 x 2 = 62 ants. After six months (2 intervals), the population is 62 x 2 = 124 ants. After nine months (3 intervals), we have 124 x 2 = 248 ants. And finally, after twelve months (4 intervals), the population will be 248 x 2 = 496 ants.