The manager of a national park determines that the park can sustain 81 coyotes. the manager assumes that the rate of change of the number of coyotes n is directly proportional to the difference between the maximum population and the current population. when t = 0, the population is 40, and t = 1, the population has increased to 60. write the population function n as a function of t.

Step-by-step explanation:

This problem can be solved by the logistic equation of populations, that is:

In which K is the carrying capacity of the population, is the initial population, r is the decimal growth rate and t is the period of time.

In this problem, we have that:

When t = 0, the population is 40: This means that .

The manager of a national park determines that the park can sustain 81 coyotes. This means that .

When t = 1, the population has increased to 60. This means that .

To write the equation, we have to find the value of r.

Now we apply ln to both sides, and:

The answer is:

126 maybe. sorry