94.6k views
3 votes
The number of insects in a colony doubles every month. There are currently 400 insects in the colony. Write an exponential expression and solve how many insects there will be after one year?

1 Answer

5 votes

Final answer:

To determine the insect population after one year given that it doubles every month, an exponential expression N = 400 * 2¹² is used, yielding 1,638,400 insects after one year of growth.

Step-by-step explanation:

The number of insects in a colony doubling every month can be represented by an exponential expression. The exponential growth formula is N = N0 * 2ⁿ, where N is the final population size, N0 is the initial population size, and n is the number of time periods (months) of growth. For the colony of insects with an initial population of 400 after one year (which is 12 months), the formula becomes N = 400 * 2¹².

To solve for N, we perform the calculation: N = 400 * 2¹² = 400 * 4096 = 1,638,400. Therefore, after one year, the insect colony will have grown to 1,638,400 insects.

User Madhusudan Joshi
by
8.1k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.