Answer Happy

Suppose that a population grows according to a logistic model with carrying capacity 6500 and k = 0.0012 per year. (a) Write the logistic differential equation for these values. dp 1 (b) Draw a direction field. Use the direction field to sketch the solution curves for initial populations of 1,000, 2,000, 4,000, and 8,000. P dt M 8000 6000 4000 2000 C TEA P 15000 10000 soont 500 1000 1500 2000 2500 3000 3500 EFF 15 000 10 000 na P 5000 8000 6000 4000 500 1000 1500
15000 10000 5000 500 1000 1300 8000 What is the significance of the inflection points? The inflection points are where the population 6000 4000 2000 @O 500 What does the direction feld tell you about the solution curves? Some of the solution curves approach 0 ast, and the others approach. All of the solution curves approach 3250 ast All of the solution curves approach 0 as r All of the solution curves approach 6500 as All of the solution curves approach as 1000 1500 2000 2500 @ 11 udend What can you say about the concavity of the solution curves? The surves with P1,000 and -2,000 appear to be concave upward everywhere. The curve with 4,000 appears to be concave downward at first and then concave upward. The curve with P8,000 appears to be concave upward everywhere. The curves with P1,000 and P2,000 appear to be concave downward everywhere. The curves with P-4.000 and P8,000 appear to be concave upward everywhere. The curves with P1,000 and -2,000 appear to be concave upward at first and then concave downward. The curve with P-4,000 appears to be concave downward everywhere. The curve with P8,000 appears to be concave upward everywhere. The curves with P1,000 and P2,000 appear to be concave downward at first and then concave upward. The curves with 4,000 and P8,000 appear to be concave upward
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) = 11 (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). P 4000 3000 2000 1000 C P 1400 1200 1000 KOO 600 400 500 1000 1500 2000 2500 3000 t P 3000 2500 2000 1500 1000 60 500 300 1000 1500 2000 2500 3000 60 P 8000 6000 4000 2000 500 1000 1500 2000 2500 3000 r G