The number of mosquitoes at the beginning of the summer was 4000. The population of mosquitoes is expected to grow at a rate of 25% a month. How many mosquitoes will there be at the end of the summer.
How many months do you consider summer?
4 months
Step 1: Calculate the number of mosquitoes after the first month.
To find the increase, multiply the current population by the growth rate:
4000 * 0.25 = <<4000*0.25=1000>>1000
To find the new population, add the increase to the current population:
4000 + 1000 = <<4000+1000=5000>>5000
Step 2: Calculate the number of mosquitoes after the second month.
To find the increase, multiply the current population by the growth rate:
5000 * 0.25 = <<5000*0.25=1250>>1250
To find the new population, add the increase to the current population:
5000 + 1250 = <<5000+1250=6250>>6250
Step 3: Calculate the number of mosquitoes after the third month.
To find the increase, multiply the current population by the growth rate:
6250 * 0.25 = <<6250*0.25=1562.5>>1562.5
To find the new population, add the increase to the current population:
6250 + 1562.5 = <<6250+1562.5=7812.5>>7812.5
Step 4: Calculate the number of mosquitoes after the fourth month.
To find the increase, multiply the current population by the growth rate:
7812.5 * 0.25 = <<7812.5*0.25=1953.125>>1953.125
To find the new population, add the increase to the current population:
7812.5 + 1953.125 = <<7812.5+1953.125=9765.625>>9765.625
Therefore, at the end of the summer, there will be approximately 9766 mosquitoes.
To determine the number of mosquitoes at the end of the summer, you need to calculate the population at the end of each month and add them up.
Given:
Initial population = 4000 mosquitoes
Growth rate = 25% per month
First, calculate the population after the first month:
Population after the first month = Initial population + (Initial population × Growth rate)
= 4000 + (4000 × 0.25)
= 4000 + 1000
= 5000 mosquitoes
Now, calculate the population after the second month:
Population after the second month = Population after the first month + (Population after the first month × Growth rate)
= 5000 + (5000 × 0.25)
= 5000 + 1250
= 6250 mosquitoes
Continue this process for the remaining months in the summer (usually 3 more months since a typical summer lasts 4 months).
Population after the third month = Population after the second month + (Population after the second month × Growth rate)
= 6250 + (6250 × 0.25)
= 6250 + 1562.5
= 7812.5 mosquitoes
Population after the fourth month = Population after the third month + (Population after the third month × Growth rate)
= 7812.5 + (7812.5 × 0.25)
= 7812.5 + 1953.125
= 9765.625 mosquitoes
Therefore, at the end of the summer, there will be approximately 9765 mosquitoes (considering rounding to the nearest whole number)