Modeling situations by combining and composing functions
- [Voiceover] Ify is building a tree tower, which is a tower built on top of a tree. The tree is currently five meters tall and Ify has found, I don't know if it's Ify or Ify, and Ify has found that it is growing by zero point one meters a month or a tenth of a meter a month. The tower is currently two meters tall. So this tower that sits on top of the tree, is two meters tall currently and Ify, or Ify, adds to it at about zero point two meters a month. So, I guess, he or she, I don't know, Ify, let's just say, "he." Is continuously building this tower on this continuously growing tree, which is fascinating. Alright, the function A of m, returns the tree's height in meters and months from now. Fascinating. The function B of m, returns the tower's height in meters and months from now. So, this is the tree's height, A of m, is the tree's height. B of m is the tower's height. Find the formula of the two functions. So, A of m, so they tell us the tree is currently five meters tall. So, it's going to be five meters tall right at the start. And then every month it is growing by zero point one meters, so it's going to be five plus zero point one times m. And this m here, this is not meters, this is actually the months. Remember, m returns, m is the number of months. So after zero months,which is right now, well this is just going to be five. After one month, it's going to be five point one. After two months it's going to be five point two. Which is exactly what we want. Alright, now let's think about the tower. So, the formula for B of m, so the tower is currently two meters tall. So, it's currently two meters tall and it grows at two tenths of a meter per month. So, two tenths times the number of months. And once again, this m right over here is not meters, I'm not writing the units here, we're just assuming whatever this returns is in meters. This m right over here is the number of months that pass by, the number of months from now. Alright, the function C of m returns the vertical distance between the ground and the top end of the tower. Makes sense, that would be from the bottom of the tree to the top of the tower. Wright the formula, C of m, in terms of A of m and B of m. Well the total height is going to be the height of the tree, which is A of m plus the height of the tower. Plus B of m, plus B of m. That's what C of m is going to be. And then they say, "Wright the formula of C of m in terms of m." Well, we just need to add these two functions. So, if we add five plus zero point one m to two plus zero point two m, that's going to be, we could add five plus two, and we'er going to get seven, plus, and if I have point one m and I add another point 2 m, that's going to be point 3 m. Zero point 3 m, and we are done. And we got it right.