Question

Suppose 10 animals are taken to an island, and then the population of these animals quadruples every 6 months. How many animals would there be after 4 years?

Answer 1

After 4 years, starting with an initial population of 10 animals that quadruple every 6 months, there would be 655,360 animals on the island.

Step-by-step explanation:

To determine how many animals there will be after 4 years when starting with 10 animals that quadruple every 6 months, we need to calculate the population growth over each 6-month period for the duration of 4 years.

1. Identify the initial population, which is 10 animals.
2. Understand the growth factor, which is the population quadrupling every 6 months. Quadrupling is the same as multiplying by 4.
3. Determine the number of 6-month periods in 4 years. Since there are 2 six-month periods in a year, 4 years contain 8 such periods.
4. Calculate the population after each six-month period. This can be done using exponential growth, where the final population is the initial population times the growth factor raised to the power of the number of periods.
5. Apply the formula: Final Population = Initial Population × (Growth Factor) No. of Periods.
   In this case: Final Population = 10 × (48).
6. Compute the final population: 10 × (48) = 10 × 65536 = 655,360 animals.

There would be 655,360 animals on the island after 4 years.