The rate of change of the population of bears is proportional to the initial population. Let P(t) be the number of bears in the population where tis measured in years. Use differential equations to nd the general solution for P(t), where P(0) is the initial population and r is the rate of growth. 0 P(t) = e'\" O P(t) = ert + P(0) o P(t) = P(0)e\" 0 Pa) =P(0)e"' \fWhat is the equation of the curve that passes through the point (1, 3) and has a slope of _2 at any point, (x, y)where a > 0? O y = e i + 60.357, x > 0 O y = ex + 60.357, x > 0 O y = Ce i, x>0 O y= 60.257e 7, x >0A radioactive isotope decays over time. A(t)is the amount of material. At t = 0 there is 15 kg and time t= 4 there is 5 kg. Write the particular solution to the differential equation which will describe the amount of isotope after time t. O A(t) : 5e{o.333)t 0 Alt) 2 1540333)! 0 A(t) = 158(0'275)' O A\") : 15e(0.2?5)t A population of endangered salmon, S (t) starts out with 40 sh and decreases proportionally at a rate of 0.01 sh per year. Let f be measured in years. Write the particular solution to the differential equation which describes the number of sh overtime. O 56) = 4040.01): 0 S(t) = met-"30* O 5(t) 2 4041101): 0 5(t) : 408{.04)t The rate of growth of wild horses is proportional to 2000 H, where H is the number of horses and is always less than 2000. Write the general differential equation to describe the number of horses, H(t), where t is in years. 0 H = 2000 033-\" O H = 2000(2h O H = 2000 l 038\" O H = 2000(3kt l Cg A bank pays continuous compounded interest. Sue deposits $100 in the account, and in 5 years she has $120. Write and solve the differential equation for A(t), the amount of money in Sue's account at time t. O A(t) = 100e(1.2)t O A(t) = 100e(0.035)t O A(t) = 1.2e(0.035)t O A(t) = 100e(-0.035)tNewton'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 Turkey at 35 degrees is placed in an oven at 350 degrees Fahrenheit, and after 30 minutes the turkey is 50 degrees. Write and solve the differential equation which describes the temperature of the turkey over time, where time is measured in hours. 0 H(t) = 350 31580'09?6t O H (t) = 35 315rFO'097m O H(t) = 50 1580'0976t o H(t) = 350 31580-09\"it A population of bees are dying at the rate proportional to the size of the initial hive, H (t), where t is measured in days. If the hive has 500 bees June 1st, and only 450 bees 15 days later, how many bees will there be 30 days later? Round your answer to the nearest bee, and assume the growth is proportional to initial population. 0 300 O 400 O 405 O 425 Assume that the rate of evaporation for water is proportional to the initial amount of water in a bowl. Jill places 1 cup and 8 ounces of water outside and notices that there is % cup of water 6 hours later. After how many hours, t, will there be less than 1 oz left? Let W(t) be the amount of water in the cup, and let t be measured in hours. Round your answer to the nearest hour. 0 t=14 O t=13 O t=12 O t=11 Bob makes coffee for his boss, Jill, every moming. Jill wants her coffee exactly 102 degrees. The coffee coming out of the pot is 140 degrees and the ofce is 71 degrees. Bob knows that after 5 minutes the coffee is 120 degrees. How long should Bob wait after making the coffee to deliver it to Jill? Use Newton's heating-cooling law, that the rate of change in the temperature, H, is proportional to the difference between the object and the surrounding temperature. 0 10.382 0 11.241 0 11.680 0 12.536 If investment A has an annual return of 4% with continuously compounded interest, and Jane has $500 after 4 years, how much money did she start out with? A(t) is the amount of money at t years. 0 426.07 0 420 O 410 O 350