Answer to Question #163400 in Trigonometry for Jellys

Question

Recent studies seem to indicate the population of North America porcupine (Erethizon dorsatum) varies sinusoidally with the solar (sunspot) cycle due to its effects on Earth’s ecosystems. Suppose the population of these species in a certain locality is modeled by the function P(t) = 250 cos ((2pi/11)(t))+ 950, where P(t) represents the population of porcupines in year t. Estimate the number of years the number of population is less than 740 animals.

Answer 1

P(t) = 250*cos(2*pi/11 + 950)

K = 2*pi/x

x = 2*pi/11

Therefore, K = 2 * pi / (2*pi/11) = 11

Max Val. = 950 + 250 = 1200

Min Val = 950-250 = 700

The average value is 1900 + 700 /2 = 950

See the figure below:

From above figure, the population less than 740 falls on point a anb b.

The interval from the above graph can be approximated to 2 years.

Final Ans. The population less than 740 comes out be approx. 2 years.