Final answer:
To calculate the number of ants after a year, we double the number of ants every 3 months. There are four 3-month periods in a year, so starting with 26 ants, they will double four times, resulting in 416 ants at the end of the year.
Step-by-step explanation:
The question asks how many ants there will be in a year if you start with 26 ants and their population doubles every 3 months. To solve this, we can use the formula for exponential growth.
Firstly, we need to determine how many 3-month periods are there in a year. Since there are 12 months in a year, there will be 12 / 3 = 4 such periods.
Next, we apply the doubling of the ant population in each period.
Starting with 26 ants, after the first 3 months, we double them, so we have 26 * 2 = 52 ants.
After the second period, we double the 52 ants, resulting in 52 * 2 = 104 ants.
Doubling again after the third period, we get 104 * 2 = 208 ants.
After the fourth and final period of the year, we double the 208 ants to arrive at 208 * 2 = 416 ants.
Therefore, after one year, there will be 416 ants.