2019 Ap Calculus Free Response Questions #1 Flow Rate FRQ Explained in Detail Pass Exam Mathgotserve

Question number one of the 2019 AP Calculus AP free response questions this presentation is focused on flow rate scenario question 1A reads it says fish enter a lake at a rate modeled by the function given by the ft equal 20 + 15 sign party or 6 by the function given by eluveitie equals 4 + 2 to the point 1 T square with EMT nlft are measured in fish per hour and sees measured in hours since midnight T equals zero birthday how many fish enters the leg over the five hour. From Midnight T equals 0 to 5 a.m. T equals five give your answer to the nearest whole number are you going to start a let's go ahead and write down the formula at that screen to guide our problem solving process okay so the formula is as follows this particular case we looking for the amount of fish that enter okay to monitor says entering so we looking at the amount added into the lake all right to the amount added what's the over a time interval amount added from to be given an ad rate what's going on I'd rates Days of our of T okay give me the address is of RP the amount added is going to be given by the equation going to be an accumulation okay accumulating the amount of fish that enters from T equals 80 T equals D of the ad rate ASMR tdt Okay let's listen to some fish in it initially in this particular case there's no fish okay so you have an initial amount the school that a sub zero as your initial amount or initial number of fish valesky's amount since it's more General all right and then you go ahead and add some more over a. Of time for me to be okay so this is the amount added amount I did the amount added is basically given by the accumulation of the address from A to B okay the T the amount added that is what we're looking for in this problem Amanda's added another thing that should be taken into consideration which is the amount of the total amount right at it and there's also the total amount so you wanted to find the total amount what are you going to do you going to find the total amount you basically combined the amount I didn't which is what we're looking for here accumulated hydrate and add that to the initial amount is Sub-Zero okay so in this particular case we just looking for we are not looking for the total amount so let's go ahead and see what the components of this function are in the will plug it into the formula okay to let start with the function the ad rate function in this particular situation there is a function for entering and there's a function for living so our ad rate east of RT is that a function sissy of T given by 20 + 15 sine of pi over 6 all right and then what are the intervals that we're looking at we are accumulating dysfunction from the lower bounds which is a 12 a.m. which is equivalent to a T-10 all the way to be the final time which is 5 a.m. T equals 5 alright let's go ahead and set up the integral to help us figure out a final answer to the amount that entered from 0 to 5 is given by the integral from 0 to 5 of EFT which is 20 + 15 sign Pine x t / 6 ETA of course so this is a calculator active part for the AP exam so you can use the gear calculator to calculate integral integral you were going to get one 53.4 5769 not the sin taxes look at that real quick for the TI-89 two different calculators approved for the AP exam policy using the TI-89 taxes he is going to hell for this particular problem you might want to story of T&L of tea in your calculator okay so you store have the phone store command so we have the function 20 plus 15 sign hi TR6 just start at in ELP okay just type it just like this store is the square button on the TI-89 you don't have to enter it over and he condensing elegant form of course of the function EFT, I want to integrate with respect to which is T and they loan limits of integration which is 0 or way of the upper limit of integration which is 5 right here okay alright so let's go ahead and write down what the answer me what the answer is and its significance in the context of this problem remember we asked to round to the nearest whole number since fractional fishes do not make sense so it's reading what the answer means the answer means that being the Mounds a fish that entered a lake enter the lake at midnight 2 a.m. to 5 a.m. is approximately 153 is 153 to the nearest whole number okay so there you have it so how was this question graded on the 2019 AP exam will this is the scoring guidelines setting up this integral expression right here correctly and you one point and then having the final answer will bring you another point to something to keep in mind is always show your Calculus okay then just too damned if I don't answer you expect to get extra credit that's that's not good whatever setup you were impotent into the calculator you must write it down as part of your work in order to receive full credit for this particular part is Reed's what is the average number of fish that live the lake per hour over to 5 hour. From pimples Reddit equals