Naturalists findthat the populations of some kinds of predatory animals vary periodically. Assume that the population of foxes in a certain forext vareis sinusoidally iwth time. REcord started being kept when time t = 0 years. A minimum number, 200 foxes, occurred when t = 2.9 years. The next maximum, 800 foxes, occured at t = 5.1 years.
come up with equation
Heres my work what did i do wrong i do not know
period = (5.1 = 2.9)2 = 4.4 years
period = (2pi)/w
w = (5pi)/(11 years)
|A| = (800 foxes - 200 foxes)/2 = 300 foxes
average foxes = |A| + Fo = 300 foxes + 200 foxes
Fo is one term represents 200 foxes
((500 foxes)5 pi)/(11 years) = (2500 pi foxes)/(11 years)
y = 500 foxes + 300 foxes sin( (5pi)/(11 years) + (2500 pi foxes)/(11 years) )
First of all, what is your question?
I will assume that you want a sinusoidal equation.
I am with you on the amplitude and period of the function.
so let it be F = 300sin(5pi/11)t
This will give us the general shape, all we have to do is to move it up and either left or right to fit the data
as it stands the max is 300 but we want our max to be 800, so let's move it up 500 to get
F = 300sin(5pi/11)t + 500
As it stands we will have a max at 1.1 (a quarter of our period of 4.4), but we want our max to be at 5.1. So we will have to move our curve from above 4 units to the right, which will give us
F = 300sin(5pi/11)(t-4) + 500
let's test it:
if t = 2.9
F = 300sin(5pi/10)(-1.1) + 500 = 200 ..... Check!
if t=5.1
F = 300sin(5pi/10)(1.1) + 500 = 800 .... Check!!!!
so
F = 300sin(5pi/11)(t-4) + 500
My denominators in the checks should have been 11 not 10, so ...
let's test it:
if t = 2.9
F = 300sin(5pi/11)(-1.1) + 500 = 200 ..... Check!
if t=5.1
F = 300sin(5pi/11)(1.1) + 500 = 800 .... Check!!!!
(I committed a typo, then cut and pasted that typo)
wtfffff did i just read yall are like geniuses
To find the equation that represents the population of foxes over time, you need to use the information given and the formula for a sinusoidal function.
First, let's find the amplitude, which is half the difference between the maximum and minimum values:
Amplitude, |A| = (800 foxes - 200 foxes)/2 = 300 foxes
Next, let's find the period of the sinusoidal function, which is the time it takes for one complete cycle:
Period, T = 5.1 years - 2.9 years = 2.2 years
The general equation for a sinusoidal function is:
y = A + Bsin(Ct + D)
In this equation:
A represents the average value of the function
B represents the amplitude
C represents the frequency of oscillation (related to the period T)
D represents a phase shift, which we'll assume to be 0 for simplicity
So, let's substitute the known values into the equation:
y = 200 foxes + 300 foxes sin((2pi)/T * t)
Since T = 2.2 years, the equation becomes:
y = 200 foxes + 300 foxes sin((2pi)/(2.2 years) * t)
Simplifying further:
y = 200 foxes + 300 foxes sin((5pi)/(11 years) * t)
Therefore, the equation that represents the population of foxes over time is:
y = 200 foxes + 300 foxes sin((5pi)/(11 years) * t)
Note: Make sure to double-check the values given in the problem to ensure the accuracy of the equation.