Question

Assuming ,P ≥0 suppose that a population develops according to the logistic equation dt / dp = 0.07P - 0.00035 P² where t is measured in weeks. Answer the following questions.

1. What is the carrying capacity?
2. What is the value of k = ?
3. For what values of P is the population increasing? Answer (in interval notation).
4. For what values of P is the population decreasing? Answer (in interval notation).

Answer 1

The carrying capacity is the maximum population size an environment can sustain. The value of K in the given equation is not provided. To determine if the population is increasing or decreasing, we need to find the range of P where the growth rate is positive or negative.

Step-by-step explanation:

1. What is the carrying capacity?

The carrying capacity, denoted as K, is the maximum population size that a particular environment can sustain. It represents the point where the growth rate of the population levels off. It is determined by the available resources in the environment.

2. What is the value of k = ?

In the given logistic equation dt / dp = 0.07P - 0.00035 P², the carrying capacity is denoted as K. However, the value of K is not explicitly provided in the equation. To find the specific value of K, additional information or data is required.

3. For what values of P is the population increasing?

The population is increasing when the growth rate, represented by dt / dp, is positive. In the given equation, dt / dp = 0.07P - 0.00035 P². To determine the values of P for which the population is increasing, we need to find the range of P where 0.07P - 0.00035 P² > 0.

4. For what values of P is the population decreasing?

The population is decreasing when the growth rate, represented by dt / dp, is negative. In the given equation, dt / dp = 0.07P - 0.00035 P². To determine the values of P for which the population is decreasing, we need to find the range of P where 0.07P - 0.00035 P² < 0.