(1 point) Find the solution to the equation in the specified region if possible. Give the answer in exact form. If a solution does not exist, write DNE in the corresponding box. a) 2 = tan(2x - 7) in (2 ) 4 Solution: b) 1 = 10 cos(2x) - 4 in (0, ") Solution: c) 10 = 5 sin (5x) in (0, #) Solution:1 point) The population of prairie dogs on Farmer Olson's land oscillates sinusoidally between a low of 700 on January 1 and a high of 1100 on July 1. 1) What is the population of prairie dogs on Farmer Olson's land on April 1? b) Find a formula for the population as a function of time, t, in months since the start of the year. Prairie dogs at time t: P(t) = Solution:(1 point) Due to recent economic uncertainty in the state of Cornellium, the interest rate one can earn by opening a savings account at Cornellium State Bank varies wildly over the course of the year. In particular, the interest rate R(t) given to new customers, where t is measured in months since January 1, 2017, is R(t) : 4.3 + 2.8 sin(%t). a) What is the period of the function ROE)? Period: 6 b) What interest rate would you earn if you opened a new account in March 2017? Interest Rate: 6.725 555 c) Which is the last month of 2017 in which you could open a new account and earn an interest rate of at least 6 percent? Month: 555 Solution