Use the following to answer problem #1 to #3. Suppose that $1500 is invested in a savings account for which interest is compounded continuously at 4.5% per year. That is, the balance P grows at the rate given by: dP = 0.045P 1) Find the function P(t) that satisfies the equation. * 5 points Add file 2) What is the balance after 3 yr? Round to the nearest cent. * 5 points3) When will an investment of $1,500 double itself? Round to one decimal 5 points place. * Your answer Use the following to answer problem #4 to #6. In January 1940, the first issue of "Flash Comics" was published. The comic book originally cost 10c. In 2018, a mid grade copy was sold for $120,000. Using two representative data points (0, $0.10) and (78, $120,000), find an exponential function that models the value V of the comic book, as given by: AP = KV 4) Find the function V(t) that satisfies the equation. Round the value of k 5 points to three decimal places. *5) Estimate the value of the comic book in 2025. Round to the nearest 5 points dollar. * Your answer 6) After what time will the value of the comic book be $1 million, assuming 5 points there is no change in the growth rate? Round to one decimal place. * Your answer Use the following to answer problem #7 and #8. In 1970, the population of polar bears in the Arctic was approximately 5,000. As of 2008, the number of Arctic polar bears had grown to about 25,000.1"} Find the function Pit) that satises the equation. Round the 1uralue of k to 5 points three decimal places. * .1. Add file 3} Predict the Arctic's polar bear population in 2029. Round to the nearest 5 points whole number. * Your answer Use the following to answer problem #9 and #10. The rumor \"People who stud}.r math all get scholarships\" spreads across a college campus. The number of students N who have heard the rumor after time t, in days. can be modeled by: 30 M\" = W 9) Find the number of students who have heard the rumor after 3 days, 7 5 points days, and 10 days. Round to the nearest whole number and separate your answers with a comma. * Your answer 10) Find the rate of change, N'(t). * 5 points t Add file Use the following to answer problem #11 to #13. In a township whose population is 8,000, an epidemic of a disease occurs. The number of people N infected { days after the disease first appears is given by: 8.000 NO= 1 + 49e-0.5t11) How many people are initially infected with the disease (t=0)?* Your answer 12) Find the number infected after 3 days, 7 days, 14 days, and 21 days. Round to the nearest whole number and separate your answers with a comma. * Your answer 13) Find the rate at which the disease is spreading after 12 days. Round to one decimal place. Be sure to include the unit "people/day". *Use the following to answer problem #14 and #15. The probability p of mastering a certain assembly-line task after t learning trials is given by: p(() = 1 -e-0.6% 14) What is the probability of mastering the assembly-line task in 1 trial? 2 trials? 3 trials? 4 trials? 5 trials? Round to three decimal places and separate your answers with a comma. * Your answer 15) Find the rate of change, p'(t). *