Question

The population of a colony of mosquitoes obeys the law of uninhibited growth. If there are 1000 mosquitoes initially and there are 1200 after 1​ day, what is the size of the colony after 22 ​days? How long is it until there are 40 comma 00040,000 ​mosquitoes? What is the size of the colony after 22 ​days?

Answer 1

Answer:

This is a simple Arithmetic Progression question, and we will use the formula:$T_{n}= a_{1} + (n-1)d$

Step-by-step explanation:

From the question, we started with 1,000 mosquitoes, this is the first term ($a_{1}$).

The next term is 1,200.

This means that the Common Difference ($d$) is:

1,200 - 1,000 = 200.

The $nth$ term ($n$) we are looking for is 22.

So we have:

$a_{1}$ = 1,000

$n$ = 22

$d$ = 200

We solve as follows:

$T_{n}= a_{1} + (n-1)d$

$T_{22}$ = 1,000 + (22-1)200

$T_{22}$ = 1,000 + (21)200

$T_{22}$ = 1,000 + 4,200

$T_{22}$ = 5,200.

So therefore, after 22 days, the number of mosquitoes in the colony will be 5,200 mosquitoes.

For the other question, we will use the value 40,000 mosquitoes.

We solve thus;

since it took 22 days to get to 5,200 mosquitoes, it will therefore take $x$ days to get 40,000 mosquitoes

22 days = 5,200 mosquitoes

$x$ days = 40,000 mosquitoes

we cross multiply thus:

22 x 40,000 = 5,200 x $x$

880,000 = 5,200$x$

making $x$ the subject, we have:

$x$ = $\frac{880,000}{5,200}$

$x$ = 169

Therefore, it will take 169 days to get 40,000 mosquitoes.