Answer Happy

Suppose that a population grows according to a logistic model with carrying capacity 6100 and k=0.0016 per year. (a) Write the logistic differential equation for these values. dtdP​=
What does the direction field tell you about the solution curves? time left. All of the solution curves approach ∞ as t→∞, 0:47:06 Some of the solution curves approach 0 as t→∞, and the others approach ∞, All of the solution curves approach 3050 as t→∞. All of the solution curves approach 0 as t→∞, All of the solution curves approach 6100 as t→∞. What can you say about the concavity of the solution curves? upward everywhere. The curve with P0​=8,000 appears to be concave upward everywhere. The curves with P0​=1,000 and P0​=2,000 appear to be concave upward at first and then concave downward. The curve with P0​=4,000 appears to be concave downward everywhere. The curve with P0​=8,000 appears to be concave upward everywhere. What is the significance of the inflection points? The inflection points are where the population − Select- ∨. (c) Use Euler's method with step size h=1 to estimate the population after 50 years if the initial population is 1,000 . (Round your answer to the nearest whole number.) P(50)= (d) If the initial population is 1,000, write a formula for the population after t years. (Use P for P(t).) Use it to find the population after 50 years and compare with your estimate in part (c). (Round your answer to one decimal place.) P(50)= (e) Graph the solution in part (d) and compare with the solution curve sketched in part (b).