Question

ant farming you have an ant farm with 25 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?

population of ants
population	25	50	100	200

the table represents a function.

Explanation:

Step1: Determine Function Type

A linear function has a constant rate of change (slope). For the table, check the ratio of population change to time change. From 0 - 3 months: $\frac{50 - 25}{3 - 0}=\frac{25}{3}\approx8.33$. From 3 - 6 months: $\frac{100 - 50}{6 - 3}=\frac{50}{3}\approx16.67$. The rates are not constant, so it's nonlinear (exponential, since population doubles every 3 months).

Step2: Calculate Ants After 1 Year

1 year = 12 months. The population doubles every 3 months. Number of 3 - month periods in 12 months: $\frac{12}{3}=4$. Initial population $P_0 = 25$. The formula for exponential growth (doubling) is $P = P_0\times2^n$, where $n$ is the number of doubling periods. So $P = 25\times2^4 = 25\times16 = 400$.

Answer:

The table represents a nonlinear function. After one year, there will be 400 ants.