Question

ant farming you have an ant farm with 22 ants. the population of ants in your farm will double every 3 months. the table shown 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
number of months: 0, 3, 6, 9
population: 22, 44, 88, 176
the table represents a nonlinear function.
after one year there will be □ ants in the ant farm

Explanation:

Step1: Determine time intervals

One year has 12 months. The population doubles every 3 months. So, the number of 3 - month intervals in 12 months is $\frac{12}{3}=4$ intervals.

Step2: Calculate population growth

We start with an initial population of 22 ants.

• After 3 months (1st interval): $22\times2 = 44$ ants.
• After 6 months (2nd interval): $44\times2=22\times2\times2 = 22\times2^{2}=88$ ants.
• After 9 months (3rd interval): $88\times2 = 22\times2^{3}=176$ ants.
• After 12 months (4th interval): $176\times2=22\times2^{4}$.

Calculate $22\times2^{4}=22\times16 = 352$.

Answer:

352