Favor

"Craig, can I ask you for a favor?" 'He didn't say anything and just nodded. "Can you teach me how you solve the problem earlier? I was fidgeting at that time because I didn't know if he would agree to my request. I shouldn't have asked him because he looks busy at the moment and with the upcoming project that we still need to discuss. "You know what? Forget about what I said and let's just start on planning on what we should do-"

"I'll help you."

"Really?" He nodded. I was shocked because I didn't expect him to comply with my request but I immediately get my paper and pen to take notes of what he will teach me.

"Okay, the problem given to you is about the Integration of Exponentials. Integration of Exponentials means that if any function is given in form f(x)= then the integration of such functions will be given as 1aeax+C where C is the constant of integration and a can be any integer. Such functions are generally used to depict the rate, growth, and decline for particular cases."

'My mind was focused when he was teaching me because I didn't want to waste a once-in-a-lifetime opportunity.

Given Data: If oil is leaking out of a ruptured tanker at the rate of r(t)=45e−0.04t thousand liters per minute, (a) At what rate, in liters per minute, is oil leaking out at t=0? at t=60? Round the answer to two decimal places and (b) How many liters leak out during the first hour? Round the answer to two decimal places.

(a) Calculating the rate at time t=0 as: r(0)=45e−0.04×0r(0)=45

Calculating the rate at time t=60min as: r(60)=45e−0.04×60r(60)=45e−2.4r(60)=4.08

(b) The total oil lost during the first 60 minutes is given as: I=∫600r(t)⋅dtI=∫60045e−0.04tdtI=−450.04[e−0.04t]600I=−450.04[e−2.4−e0]I=−450.04[0.907−1]I=1022.94liters

'I was in awe of how good he is at explaining and he showed me the steps on how he had gotten the correct answers to the given data. He taught me his own method and to be honest, his way of solving problems is simpler but accurate.'

'After teaching me, I discuss with him my ideas for the project.' "I was thinking that our story will revolve around two childhood friends who are both in love with each other but are not being vocal with their feelings because they are both afraid to take risks and bounded by what-ifs." 'I was not sure if he will like my idea but I was kinda hoping that he will because 5 months may seem a long time, but time flies quickly. Also, we will need to focus on conceptualizing the script, finding locations, and filming it.'

"Let's go with it. It might be a bit different to what our classmates will do but different is good."

"Different is good," 'Both of us chuckled at the same time after realizing that we said the same thing. He was the one who quickly went back to normal, so I took that opportunity to tell him about my other plans.' "What we need to do is conceptualize the script, find locations, hire two actors, and film it."

"But, where will we get the actors that will be part of the video. We can't just hire anyone, it would be better if they are a real couple for them not to feel awkward with one another and for the script not to look too scripted. They will need to be able to showcase the depth of their real feelings and convey the emotions that will be shown in the video after reviewing the script."

'I didn't expect Craig to know so much and also give a lot of insights because I'm used to him giving me short answers or better yet, he's just nodding.' "Well, for now, let's focus first on the script and in finding locations. In the script, I want to add a scene where the two childhood friends are in their prime and they have this bucket list of things that they want to accomplish together. As they try to finish everything that is in the list, day by day their feelings are growing deeper, but neither are them are speaking about their true feelings because they are afraid to lose their friendship, to take risks, and are bounded by what-ifs."

"I like that and what I want to see in the video is that they will not rely on the script. They will only do the things that are written on it which are part of the bucket list that is needed to be accomplished, and their conversation is all improvised or on the spot for it to look realistic."

'Craig is right. For this to work, we really don't need a lengthy script because we need to focus on their interactions and how can they show love in all those places.' "Do you know any romantic place that can be found here in New York, Craig?"

"I don't really go out that much, all I know is that the place I frequently visited when I was a child is the Top of the Empire State Building. How about you? Do you know any romantic spots that are found in New York?"

I nodded at him. "Actually, while I was cooking I browse the internet and I saw some spots that pique my interest and they are the Staten Island Ferry, Brooklyn Botanic Garden, Shakespeare Garden, Domino Park, Hayden Planetarium, and the Red Hook and the Columbia Street Waterfront. I took a screenshot of all the places and every time I scroll down these places are all on top that should be visited by couples."

"Ok, Do you think we could film here?"

"I'm not sure but maybe if we call the owners of each place that we will pick, and inquire them about the price of how much is needed to be paid and see if they will allow us to film in their place."

'That's what we did in our free time. Craig is in charge of calling the owners of each place and thankfully they all agreed, while I was assigned to finalize the script. I also wrote what I want them to do in each scene that is part of the bucket list because, in all of those places, there is one important trait that is needed to be showcased and that is love.'

Part of the Bucket List to be accomplished are: (1) Visit the Top of the Empire State Building (2) Ride the Staten Island Ferry, (3) Take a picture of all the beautiful flowers in Brooklyn Botanic Garden, (4) Strolling at the Shakespeare Garden, (5) See the incredible view of the Williamsburg Bridge in Domino Park, (6) Stargazing at the Hayden Planetarium, and (7) Watch the sunset at the Red Hook and Columbia Street Waterfront.

'I can't believe that in that short amount of time we were able to do a lot and I must say our progress is most likely at 50%. All that's left to be done is hiring actors and filming it.'