The population of a colony of mosquitoes grows exponentially according to the function P (t) = P0ekt.

a) If there are 1,000 mosquitoes initially and there are 1800 after 1 day, what is the size of the colony after 3 days?

b) How long will it take the colony to reach 10,000 mosquitoes?

The answer to your question is:

a) P (3) = 5818 mosquitoes

b) 4 days

Step-by-step explanation:

Data

P (t) = Poekt

a)

Po = 1000 mosquitoes

Pt = 1800

t = 1 day

P (3) = ?

1800 = 1000 e1k

1800 / 1000 = e 1k

e 1k = 1.8

1k = In 1.8

k = 0.587

P (3) = 1000 e (0.587) (3)

P (3) = 1000 e 1.761

P (3) = 5818. 2 mosquitoes

b)

P (t) = 10,000

10000 = 1000 e 0.587t

10000 / 1000 = e 0.587t

10 = e 0.587t

In 10 = in e 0.587t

2.3 = 0.587t

t = 3.92 days ≈ 4 days