Question

part 2 of 2
ant farming you have an ant farm with 26 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	26	52	104	208

the table represents a nonlinear function

after one year there will be \\(\square\\) ants in the ant farm

Explanation:

Step1: Verify linearity (rate check)

Check population change per 3 months:
$52-26=26$, $104-52=52$, $208-104=104$
The change is not constant, so it is nonlinear.

Step2: Identify growth pattern

Population doubles every 3 months: $P(n) = 26 \times 2^{\frac{n}{3}}$, where $n$ = months.

Step3: Calculate 1-year (12 months) population

Substitute $n=12$:
$P(12) = 26 \times 2^{\frac{12}{3}} = 26 \times 2^4$
$2^4=16$, so $26 \times 16 = 416$

Answer:

The table represents a nonlinear function
After one year there will be 416 ants in the ant farm