Question

ant farming you have an ant farm with 34 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 number of months 0 3 6 9 population 34 68 136 272 the table represents a nonlinear function. after one year there will be \\(\square\\) ants in the ant farm.

Explanation:

Step1: Determine the growth pattern

The ant population doubles every 3 months. Initial population \( P_0 = 34 \). The time period for doubling is \( t_d = 3 \) months.

Step2: Calculate the number of doubling periods in a year

A year has 12 months. Number of doubling periods \( n=\frac{12}{3}=4 \).

Step3: Calculate the population after 4 doubling periods

The formula for exponential growth (since population doubles each period) is \( P = P_0\times2^n \). Substituting \( P_0 = 34 \), \( n = 4 \), we get \( P=34\times2^4=34\times16 = 544 \).

Answer:

544