Question

On a certain swampy island, the population of mosquitos increase in proportion to the number present. left undisturbed this population would double every five days. when the population of mosquitoes is 110,000 a group of 20 bats is introduced onto the island. these bats each consume mosquitos at a constant rate of 800 per night. because they have no predators and do not have time to reproduce over the course of several weeks, the bat population does not change. how long before the population of mosquitos is reduced to 30,000? what happens in the same amount of time if the bats are introduced when the mosquito population is 120,000?

Answer 1

we need to know how much time takes to reduce the population to 30.000 mosquitos. So, 110.000 -30.000 is the amount of mosquitos consumed, it is 80.000. Then, if 1 bat consumes 800 mosquitos per night, then 20 bats consume 16.000 mosquitos per night.

So, in one night they consume 16000 mosquitos, then in how many nights they consume 80.000?

1 night --------- 16000 mosquitos

x= 5 nights---------- 80.000 mosquitos

So to reduce population to 30.000 it takes 5 nights.

Now for the second question, bats will have the same capacity to eat mosquitos, so, in the sae amount of time (5 nights) they will consume 80.000 mosquitos. Then if the initial amount is 120.000, the population will be reduced to: 120.000-80.000= 40.000 mosquitos.