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.

May

Accepted Answer

Mhm. Hey everyone. Welcome back in this problem. We're told that in a certain university, the number of students who participated in the yearly fundraising activity from 2011 to 2018 can be modeled by A FX is equal to three X squared minus 52 X plus 255. Where X equals one represents the year 2011 from 2018 to 2022. The number of students is represented by A FX equals 42 X minus 305. We're asked to calculate the number of students who participated in the activity in 2015. We're given four answer choices. Option A 51 option B option C 126 and option D 70. Now 2015. OK. Falls in between 2011 and 2018. And so the function we're gonna be using to model the number of students is the first function we were given. OK. A FX is equal to three X squared minus 52 X plus 255. Now, in order to determine the number of students who participated, we need to find the X value that we should be using. OK to evaluate a, the number of students. Now, we know that 2011 is represented by X equals one. That means that the next year 2012 is represented by X equals two. And you can continue this pattern to find that 2015 is going to be represented by X is equal to five. So what we want to find is our a value, the number of students when X is equal to five. So we have a, at five is equal to, we're gonna substitute five into this equation. Everywhere we have an X, we get three multiplied by five squared minus 52 multiplied by five plus 255. This gives us three multiplied by minus 260 plus 255. Three multiplied by 25 is 75. We have negative 260 plus 255 which is negative five. So we get 75 minus five, which is equal to 70. And so in 2015, which was represented by X equals five, we have 70 students who participated in the fundraising activity. This corresponds with answer choice D. That's it for this one. Thanks everyone for watching. I hope this video helped.

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