Question

The population of a colony of mosquitoes obeys the law of uninhibited growth. If there are 1000 mosquitoes initially and there are 1300 after 1​ day, what is the size of the colony after 4 ​days?

Answer 1

Answer:

2,855 is the size of the colony of mosquitoes after 4 ​days.

Explanation:

The law of uninhibited growth is given as:

$A=A_o\times e^{k\times t}$

$A_o$= Original amount

A = Amount after time t

k = Positive constant repressing the rate of growth

We are given with:

Original population of mosquitoes = 1000

Population of mosquitoes after 1 day =1300

t = 1 day

$1300=1000\times e^{k\times 1 day}$

$k = 0.2623 day^{-1}$

Population size of mosquitoes after 4 days

$A_o=1000, k= 0.2623 day^{-1}$

A =? , t = 4 days

$A=1000\times e^{ 0.2623 day^{-1}\times 4 days}$

A =2,855.36 ≈ 2,855 mosquitoes

2,855 is the size of the colony of mosquitoes after 4 ​days.

Answer 2

Answer:

$2855$

Explanation:

As per the law of uninhibited growth

Population after a time period of "t" will be given by

$P(t)= P_0e^{kt}$

where,

$P_0$ is the initial population.

k is the growth rate

Growth rate of mosquitoes

$1300= 1000*e^{k*1}\\e = 0.2623$per day

So, population of mosquitoes after four days will be

$= 1000* e^{0.2623*4}\\=1000*2.855 \\= 2855$