Your research adviser for an ecology project tells you to create a population mo

Question

Your research adviser for an ecology project tells you to create a population model for a specific species of insects. She gives you the following basic information about the species population in Minnesota:

The size of the population seems to be periodic with a period of one year.

The population is always largest on August 1 and smallest on February 1.

The average population (usually achieved on May 1 and Nov.~1) is approximately 2.48 million insects in Rice County.

The peak population is estimated to be 20% larger than the average population.

Create a function that models the population of the insects at time t, where t=0 is January 1 and t=11 is December 1. Write down the function and explain how you deduced it.

Explanation / Answer

GIVEN INFORMATION:

a) The model is periodic and repeats for a period of 1 year, that is, every year it follows the exact same pattern.

b) Largest - August 1, Smallest - February 1

c) Average population (on May 1 and Nov 1) = 2.48 million

d) Peak (Largest) population is 20% larger than average population -> Population on Aug 1 : 120/100 x 2.48M = 2.976 million

To create the function that models this trend, we essentially use the two point form. Since we know the populations on two different dates -->

May 1 -> t = 4, P = 2.48M

Aug 1 -> t = 7, P = 2.976M

Nov 1 -> t = 10, P = 2.48M

Slope of the line = P2 - P1 / t2 - t1 = 2.976 - 2.48 / 7 - 3 = 0.496/4 = 0.124

Two point formula :

P - P1 = slope x ( t - t1)

P - 2.48 = 0.124 x ( t - 4 )

P = 0.124t + 1.984

As the slope is positive, this line increases in P with increase in t -> the population is increasing as t is increasing. But we know this happens only from February to August, and it goes from high to low from August to February.

Therefore, ANSWER =

P = 0.124t + 1.984 from t = 1 to t = 7

P = -0.124t + 1.984 from t = 7 to t = 1

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.