restart;Calc I Maple Lab # 1Due on Wednesday, February 1 at 5 pm.You must work in teams of two and no team may have more than two members.Some Reminders:(a) There is a Maple worksheet for almost every section we covered in class, located in the folder P:\134Calc1. All you need to do is open them and click through. You can even cut and paste from them to your own worksheet.(b) You may add execution groups in places where you would need them.(c) Document your work. Comment on what you are doing and why. Be sure to understand the steps you are taking when solving a problem. State your conclusion/answer.(d) Please proofread your work before you submit it. The first thing that the grader will do is execute ALL of your commands (by clicking !!! on the toolbar above). Make sure that she will she what you intends her to see.(e) Help save paper. Shrink your graphs moderately before you print (if you need to print the worksheet).(f) Upload your work in moodle. Only one submission needs to be done per group.(g) Maple has very short memory. Execute ALL your commands by clicking on the !!! icon on the toolbar above EVERYTIME you open your worksheet.PROBLEM # 1: Zika virus is primarily spread through the bite of an infected Aedes species mosquito; it can also be transmitted sexually, or through a blood transfusion, or from a mother to her baby during pregnancy (Montgomery County, PA official website). The number of reported infection in Pennsylvania is modeled by the function Z(t)=1*1.63t where t is in months since February 23, 2016.(a) Here we type in the formula for the infection growth of the virus. Take note of the proper syntax of naming the functionZ:=t->1*1.63^t;(b) How many would be infected by May 23 (t=3 months)?Solve: 1*1.63^(3)(c) How many will be infected after one whole year?Solve: 1*1.63^(12)After one year, there will be approximately ____351_____ people infected by the virus.(c) By plotting the function you have above AND the horizontal line passing through the point (0, 10000), estimate when will the number of infected people reach 10,000(you have to choose a good viewing window here to get a good estimate). Complete the command below by filling in the missing parts.plot({Z(t),10000},t= .. );Estimated time based on the graph: _________________________________.(d) By guess and check, estimate the time until the number of infected people is 10,000.C( );C( );C( );C( );Estimated time based on the guess and check method: _______________________.(e) Use the solve command of Maple to find the actual time it takes for the virus to infect 10,000 people.solve(Z(t)=10000,t);Answer given by the solve command (rounded to three decimal places): PROBLEM # 2: Anthony has some reading to do for his psychology class. After reading for 12 minutes, he checked to see how many more pages he needs to read and found that he still has 31 pages left to read. After 48 minutes of reading, he counted that he has 4 more pages to read.REMEMBER: Document your work. Use the example given in (a) as your guide.(a) How fast is Anthony reading? In other words, how many fewer pages does he need to read if he reads for one minute?Type in the appropriate Maple command in the execution group below and execute it. Also, complete the sentence below to describe what the Maple command you have solves with respect to the formula of a linear function.Anthony's reading speed is___________.The answer I obtained above is the ___________ of the linear function.(b) How many total number of pages did he need to read?(c) Write an equation for the number of pages left to read in terms of the number of minutes Anthony has been reading.(d) Plot the function you have in (c).(e) How many minutes have Anthony been reading if he has 26 more pages to read?GRAPHICALLY:USING GUESS AND CHECK:USING MAPLE'S solve COMMAND:PROBLEM # 3: (a) Does the function 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+2 have an inverse? Justify your answer by plotting f(x) and explaining what the graph tells you.Answer and explanation: ______________________(b) Are 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JSFH and 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 inverses of one another? Why or why not? Justify your answer by plotting f(x) and g(x) in one coordinate system, together with the line y=x.Answer and explanation: ___________________(c) What is the inverse of f(x) (you may do this by hand if you wish)? Justify your answer graphically, that is, by graphing f and its inverse h (we are giving the inverse of f the name h), together with the line y=x and describing what you see.JSFHAnswer and explanation: _______________________.