A rate of change of H is given by % 2 H15 4H). When t = D, H = 20. When t = 2, H = 50. Solve for k where H > -'15. O 0.31 O 1.208 O 2.232 O 3.282 Newton's heating-cooling law states that the rate of change in the temperature, H, is proportional to the difference between the object and the surrounding temperature. Let H(t) be the temperature of the object being heated and S be the surrounding temperature. A cold object at 35 degree is placed in an oven at 350 degrees Fahrenheit and after 30 minutes the object is 100 degrees. Write and solve the differential equation which describes the temperature of the object over time, where time is measured in hours. 0 H(t) = 350 woe-\"452% O H(t) = 100 3580'4622t O H\") = 350 _ 315eD.422t O H(t) = 100 3153-0-46\" Sue's grade in her math class is related to the number of hours she studies. The rate of change of her grade, G0), is proportional to (100 - G), wheret is measured in hours and G(t) is her grade after t hours of study. The highest grade is a 100. {3(0) = 60, meaning she could get a 60 without any studying. After 10 hours Sue's grade would be an 80. How many hours would Sue need to study to get an A, which is a 90 or better? Round your answer up to the nearest hour. 0 12 20 O 25 030 If a population of endangered salmon, S{t), starts out with 80 sh and decreases at a rate proportional to 0.02 times the number of sh present each year, what is the particular solution to the differential equation which describes the number of sh over time? Let t be measured in years. 0 S(t) = 8089.02): 0 S(t) 2 8040112): 0 S (t) = Ethel0'2)t o S(t) = 10060-02)t If investment A has continuously compounded interest and an annual return of 2%, and Jane has $100 after 5 years, how much money did she initially invest? Round to the nearest dollar. 0 75 O 81 O 90 095 A population of honey bees is dying at the rate proportional to the size of the initial hive, H(t), where t is measured in days. If the hive has 800 bees at the start of the summer and only 600 bees 90 days later, how many bees will there be 200 days from the start of summer? Round your answer to the nearest bee and assume the growth rate is proportional to the population at a given time. 0 522 O 422 0344 ("1 if\