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Chapter 5: Q 5 (page 335)

Growth of a Colony of Mosquitoes

The population of a colony of mosquitoes obeys the law of uninhibited growth.

(a) If N is the population of the colony and t is the time in days, express N as a function of t.

(b) If there are 1000 mosquitoes initially and there are 1800 after 1 day, what is the size of the colony after 3 days?

(c) How long is it until there are 10,000 mosquitoes?

Short Answer

Expert verified

(a) N as a function of t can be expressed as Nt=N0ekt

(b) Size of the colony after 3 days will be 5832

(c) It will take 3.9 days for the population to be 10,000

Step by step solution

01

Step 1. Given information

The population of a colony of mosquitoes obeys the law of uninhibited growth.

02

Part (a)  of step 1.  N as a function of t. 

If N is the population of the colony and t is the time in days, then N as a function of t can be expressed asNt=N0ekt

03

Part (b) of Step 1. Size of the colony after 3 days  

Substitute Nt=1800,N0=1000,t=1, in the function

role="math" localid="1647280123581" Nt=N0ekt1800=1000ek脳11.8=ekln1.8=lnekln1.8=kk=0.58779

Now substitute N0=1000,k=0.58779,t=3in the function

Nt=N0ektNt=1000e0.58779脳3Nt=1000脳5.832Nt=5832

The population of the colony after 3 days will be 5832.

04

Part (c) of Step 1. Time required for the population to be 10,000

Substitute Nt=10000,N0=1000in the function

role="math" localid="1647280306723" Nt=N0e0.58779t10000=1000e0.58779t10=e0.58779tln10=lne0.58779tln10=0.58779tt=ln100.58779t=3.9

The time required for the population to be 10,000 is 3.9 days

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