Solve each problem. During the course of ayear, the number of vol...

Question

Solve each problem. During the course of ayear, the number of volunteers available to run a food bank each month is modeled by V(x), where V(x)=2x^2-32x+150 between the months of January and August. Here x is time in months, with x=1 representing January. From August to December, V(x) is mod-eled by V(x)=31x-226.

Find the number of volunteers in each of the following months.

August

Accepted Answer

Hey, everyone in this problem in a certain university, the number of students who participated in the yearly fundraising activity from 2011 to 2008, 18 can be modeled by A FX is equal to three X squared minus 52 XX plus 255 where X equals one represents the year 2011 from to 2022. The number of students is represented by A FX is equal to 42 X minus 305. We're asked to calculate the number of students who participated in the activity in 2018. We're given four answer choices, option A 51 option B option C 31 option D 126. Now we're interested in the year 2018 2018 is actually included in the range of years for both of the functions we're given. OK. So how do we decide which one to use? Well, let's go ahead and try both of them and see what we get. Now in order to substitute in a value to find the number of students a we need to know what X should be. OK? So we're told that X equals one represents 2011. And that means that X equals two, represents 2012. We can carry this pattern on, then X equals eight will represent 2018. OK? So we wanna use an X value of eight in these functions that we were given. Now, let's start with the first function and we're told that from 2011 to 2018, we can use a FX is equal to three X squared minus 52 X plus 255. Substituting in our X value of A, we have a evaluated at A is equal to three multiplied by eight squared minus multiplied by eight plus eight squared gives us 64 multiplied by three is 192. So we have 192 minus plus 255. And if we simplify, add those all up, we get that A of A is equal to 31. OK. So when we use the first equation, we get that 31 students participated in the year represented by X equals eight, which is the year 2018. Now, if we use the other equation which we're told is valid for 2018 to 2022 we have a of X is equal to X minus 305. OK. Substituting in that X value of eight, we have a evaluated at eight is equal to multiplied by eight minus 305. Ok. 42 multiplied by eight minus 305 gives us 31 as well. OK. And so 18 was included in the range for both of these functions. OK. So they're both valid and they both gave us the same answer. And so we don't need to worry about which one we should have been using. Both are. OK. We found that the number of students who participated in this activity in 2018 is 31 which corresponds with answer choice. C thanks everyone for watching. I hope this video helped see you in the next one.

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