The population of a colony of mosquitoes obeys the law of uninhibited growth. if there are 1000 mosquitoes initially and there are 1700 after 1 day, what is the size of the colony after 4 days? how long is it until there are 70,000 mosquitoes?

The size of the colony after 4 days is 8351.15.

8 days long there are 70,000 mosquitoes.

Step-by-step explanation:

Given : The population of a colony of mosquitoes obeys the law of uninhibited growth. If there are 1000 mosquitoes initially and there are 1700 after 1 day.

To find : What is the size of the colony after 4 days and How long is it until there are 70,000 mosquitoes?

Solution :

Let the uninhibited growth is defined by a function,

Where, is the initial amount

e is the Euler's constant

k is the amount of increase

t=1 day is the time

A=1700 is the amount

Substitute all the values in the formula,

Taking natural log both side,

Now, The size of the colony after 4 days is

Therefore, The size of the colony after 4 days is 8351.15.

When there are 70,000 mosquitoes the time is

Taking ln both side,

Therefore, 8 days long there are 70,000 mosquitoes.

1

step-by-step explanation:

it's the only multiple of both and the least