Homework: Section 4.2 & 4.3 p1 Question 13, 4.3.39-LS > HW Score: 67.31%, 8.75 of 13 points O Points: 0 of 1 Save The population of an aquatic species in a certain body of water is approximated by the logistic function Ay 22,500 30,000- G(t) = 1+ 15 e - 0.67t . Where t is measured in years. 20,000- G (t) Calculate the growth rate after 7 years. 10,000- 0 4 8 12 16 20 The growth rate in 7 years is | . (Do not round until the final answer. Then round to the nearest whole number as needed.)5 Inx + 8 The function f(x) = has a relative extreme point for x > 0. Find the coordinates of the point. Is it a relative maximum point? X Identify how to find the extreme values of the function and the derivative of the function required to find it. Select the correct choice below and fill in the answer box to complete your choice. O A. The extreme values are always found by substituting 0 for x in the first derivative. The first derivative is f'(x) =. O B. The extreme values occur at the x-coordinate where the first derivative is equal to 0. The first derivative is f'(x) = O C. The extreme values occur at the x-coordinate where the second derivative is equal to 0. The second derivative is f"(x) = O D. The extreme values are always found by substituting 0 for x in the second derivative. The second derivative is f"(x) =.Question 10, 5.1.37-LS HW Score: 79.16%. 7.92 of 10 points Part1 of5 0 Points: 0 of1 Homework: Section 5.1 p1 A person is given an injection of 400 milligrams of penicillin at time t = 0. Let f(t) be the amount (in milligrams) of penicillin present in the person's bloodstreamt hours after the injection. Then, the amount of penicillin decays exponentially. and atypical formula is f(l) : 400 e _ 0 41. Complete pans (a) through (0) below. (a) Give the differential equation satised by f(t). f'(t):D Let P(t) be the population (in millions) of a certain city t years after 2015. and suppose that P(t) satisfies the differential equation P'(t) = 0.03P(t), P(O) = 2. (3) Use the differential equation to determine how fast the population is growing when it reaches 5 million people. (b) Use the differential equation to determine the population size when it is growing at a rate of 800,000 people per year. (c) Find a formula for P(t). D. Solve P'(5) = 0.03%) for P(t). The population is growing at about 0.15 million people per year when it reaches 5 million people. (Type an integer or decimal rounded to two decimal places as needed.) (b) Choose the correct process to nd the population size when it is growing at a rate of 800,000 people per year. A. Evaluate P'(t)= 0.03P(0.8). .V B. Solve 0.8 = 0.03P(t) for P(t). C. Evaluate P'(t)= 0.03(0.8). D. Solve P'(0.8) = 0.03%) for P(t). The popu ation size is about 26.67 million people when it is growing at a rate of 800,000 people per year. (Type an integer or decimal rounded to two decimal places as needed.) (0) PM = (Type an expression using t as the variable.) Homework: Section 51 p1 HW Score: 79.16%, 7.92 of 10 points Part 2 org 9 Points: 0.06 of 1 A sample of 15 grams of radioactive material is placed in a vault. Let P(t) be the amount remaining after t years: and let P(t) satisfy the differential equation P'(t) : 0.036P(t). Answer parts (a) through (9). (a) Find the formula for P(t). Pm = 15e '0'036' (Type an expression using t as the variable.) (b) What is 13(0)? P(0) = E Homework: Section 5.1 p2 Question 5, 5.1.37-LS HW Score: 62.5%, 5 of 8 points Part 1 of 5 O Points: 0 of 1 Save A person is given an injection of 600 milligrams of penicillin at time t= 0. Let f(t) be the amount (in milligrams) of penicillin present in the person's bloodstream t hours after the injection. Then, the amount of penicillin decays exponentially, and a typical formula is f(t) = 600 e - .. Complete parts (a) through (c) below. (a) Give the differential equation satisfied by f(t). f' (t) =E Homework: Section 5.1 p2 Question 7, 5.1.43-LS HW Score: 62.5%, 5 of 8 points Points: 0 of 1 Save X In an animal hospital, 10 units of a certain medicine were injected into a dog. After 45 minutes, only 4 units remained in the dog. Let f(t) be the amount of the medicine present after t minutes. At any time, the rate of change of f(t) is proportional to the value of f(t). Find the formula for f(t). The formula is f(t) =. (Use integers or decimals for any numbers in the equation. Round to three decimal places as needed.)