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Problem 3: When Norway rats invade a new warehouse where living conditions are ideal, they multiply...

Problem 3: When Norway rats invade a new warehouse where living conditions are ideal, they multiply at a very rapid rate: r=0.0147 per day. How many days are required for the population size to double?

How many rats will be in the population after 80 days?

For part A I got:

Nt = N0ert

2 = 1 (ert) (take natural log of both sides)

ln (2) = r * t (divide both sides by r)

ln(2) / r = t

= ln(2)/0.0147 = 47.14 days for the rat population to double

I just need to know how many after 80 days

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Answer #1

Given rate r = 0.0147 per day

Exponential growth Nt = N0ert

N0 = Initial number of individuals

Nt = Number of individuals at time, t

t = time

Doubling time t = ln2/r = 0.693/0.0147 = 47.14 days.

So, at the end of 47.14 days, the population of the rat doubles.

At the end of 80 days,

t = 80 days ; r= 0.0147 ; N0 = 1 (initial number of rats) ; Nt = ? (Final number of rats)

Nt = N0ert = 1 x e0.0147x80 = 1 x e1.176 = 1 x 3.24 = 3.24

At the end of 80 days, the number of rats present will be 3.24 times the number of initial rats.

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