Question

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?

Answer 1

Answer:

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