Name                                     MATH 116 PRACTICE MIDTERM 1 Please work out each of the given problems.  Credit will be based on the steps that you show towards the final answer.  Show your work. PROBLEM 1  Find the derivative of the following functions A.    f(x)  =  ln(ln x)    B.      C.       PROBLEM 2  Find the following anti-derivatives. A.     B.      C.       PROBLEM 3  During an experiment with a deadly new virus, Tom drops a flask of the virus on the floor.  Tom and his four lab aids are immediately infected.  During the next six hours they infect an additional forty unsuspecting people.  Assume the rate of spreading of the virus is proportional to the number of people who have been infected. A.  Write a differential equation that models this situation.  Be sure to label your variables.   B.   How long will it be until one million people have been infected?     PROBLEM 4  A population of bacteria is growing at the rate of          dP              3000                 =                                     dt            1 + 0.25t where t is the time in days.  When t = 0, the population is 1000.  A. Write an equation that models the population P in terms of the time t.   B. What is the population after 3 days?   C. After how many days will the population be 12,000?     Extra Credit:  Write down one thing that your instructor can do to make the class better.