LESSON 9 A quantitative look at the fish population Now you'll study the same fish population as in Lesson 8, but this time you'll answer some quantitative questions. Recall that the fish population, p(t), satisfies the DE p' = p - 0.2p² - 0.7, (fishpop) where p is measured in thousands of kilograms and t is in weeks. The above DE has two equilibrium populations, p₁=0.8 and p₂ = 4.2, both of which are constant solutions of the equation. Since they're solutions, no other solution can cross through them; this can be seen by applying the Existence and Uniqueness Theorem (see your text) to the problem. Thus, the other solutions either approach them asymptotically as t-, or move away from them. Your phase line plot from the last lesson should show this. Task 1. Use the Euler approximation method with a reasonable step size to answer the following questions. 1. If p(0) = 6 (i.e., 6,000 kg), what is the population after 10 weeks? 2. How close is this to the equilibrium point it's approaching? 3. At about what time does the population stop dropping by 100 kg per week? 4. When does the population come within 50 kg of equilibrium?

Can balloons hold more air or more water before bursting? A student purchased a large bag of 12-inch balloons. He randomly selected 10 balloons from the bag and then randomly assigned half of them to be filled with air until bursting and the other half to be filled with water until bursting. He used devices to measure the amount of air and water was dispensed until the balloons burst. Here are the data

Physics written by hand.

·l S eDrive 2 F2 W S - Save & Exit Certify Lesson: 3.2 The Chain Rule and the Genera... Question 16 of 16, Step 2 of 2 13/18 Correct It is estimated that t years from now the population of a city will be P(t) = 20(60 + 3t)² - 1100t. Step 2 of 2: Find the rate of change in population in 7 years. Answer How to enter your answer (opens in new window) people/year < Previous X #3 80 F3 E D 69 + 4 C 888 R LL % 5 V F5 T G 6 MacBook Air Fo Y B & 7 H Da F7 U N * 00 8 J DII FB ( - 9 T K F9 M O ) O < E H F10 P OLIVIA LIPSCO Ke - Submit Answer F11 Keyboard Sh A + "1 { [ L A V =