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:

first, we define the variables:

x: number of years after 1950

f (x): amount of vinyl sold.

then, with the variables defined, we have:

68594 vinyl records were sold in 1958 > f (8) = 68594

91299 vinyl records were sold in 1961 > f (11) = 91299

38720 vinyl records were sold in 1952 > f (2) = 38720

161743 vinyl records were sold in 1967 > f (17) = 161743

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step-by-step explanation:

step-by-step explanation: