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(a) If you add 2 ounces of 40°F cream to the 180°F coffee in the cup, how long will it take for themixture to reach drinking temperature? Give your answer (in minutes) in decimal form with at least 3decimal digits (for example, 12.345 minutes). 16.033 16.03261minutes (b) If you let the 12 ounces of 180°F coffee cool for 5 minutes before adding 2 ounces of 40°F cream,how long will it take (after the initial timewhen the coffee was 180°F) for the mixture to reach drinkingtemperature? Give your answer (in minutes) in decimal form with at least 3 decimal digits (for example,12.345 minutes). 15.760 15.75983minutes (c) In order to reach drinking temperature as quickly as possible, should you add the creamimmediately, or wait 5 minutes? you should add the cream immediatelyyou should wait 5 minutes
11/17/14, 2:19 PMMath 125 HW_9CPage 8 of 87.9/9 points | Previous AnswersA person borrows $10,000 and repays the loan at the rate of $2,400 per year. The lender chargesinterest of 10% per year. Assuming the payments are made continuously and interest is compoundedcontinuously (a pretty good approximation to reality for long-term loans), the amount M(t) of money (indollars) owed tyears after the loan is made satisfies the differential equation and the initial condition(a) Solve this initial-value problem for M(t). M(t) = (b) How long does it take to pay off the loan? That is, at what time tis M(t) = 0? Give your answer (inyears) in decimal form with at least 3 decimal digits. 5.390 5.389965years= M−2400dMdt110M(0) = 10000.