The per capita growth rate of many species varies temporally for a variety of reasons, including seasonality and habitat destruction. Suppose n(t) represents the population size at time t, where n is measured in individuals and t is measured in years. Solve the differential equation for habitat destruction and describe the predicted population dynamics. n′=(e−t−1)nn(0)=n0 Here the per capita growth rate declines over time, starting at zero and becoming negative. It is modeled by the function e−t−1.

Step-by-step explanation:

If n(t) represents the population size at time t, where n is measured in individuals and t is measured in years.

Taking the integral of both sides

ln |n| =

Where C is integration constant

Taking the exponential of both sides

whee the exponential of a constant is a constant K.

When t=0,

Therefore:

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

eventually after a few more steps, your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x