Final answer:
The question asks about the exponential growth of a mosquito population. Given an initial population of 1,000 mosquitoes which grows to 1,400 after one day, the growth rate can be determined. Using this growth rate, the population after 2 days is calculated to be approximately 1,960 mosquitoes.
Step-by-step explanation:
The subject of this question is exponential growth, specifically referring to the law of uninhibited growth. This is a mathematical concept frequently observed in biology, particularly in scenarios such as the growth of a colony of mosquitoes or bacteria. The main concept of exponential growth is that the growth rate - the number of organisms added in each generation - is increasing at a greater and greater rate.
Given the circumstances of the problem, including an initial mosquito population of 1,000 and a population of 1,400 after 1 day, we are observing exponential growth. This means that the population size is increasing at a rate that gets faster over time. To understand how much the population would increase by the next day, we can use the formula for exponential growth: Population = Initial Population * e^(rate of growth * time), where e is the mathematical constant.
Firstly, we need to calculate the rate of growth based on the information given. We know that the population grew from 1,000 to 1,400 in one day, so the growth rate can be calculated by rearranging the formula to: rate of growth = ln(Population/Initial Population)/time. Substituting the values in, we get rate of growth = ln(1400/1000)/1, which is approximately 0.336. Now, we use this growth rate to calculate the population size after 2 days by substititing values back into the original formula: Population = 1000 * e^(0.336 * 2), which evaluates to approximately 1,960. So, the size of the mosquito colony after 2 days would estimatedly be around 1,960 mosquitoes.
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