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# Modeling with function combination

CCSS.Math:

## Video transcript

if he is building a tree tower which is a tower built on top of a tree the tree is currently five meters tall and if he has found it out if he or I fee and if he has found it is growing by 0.1 meters a month or a tenth of a meter month the tower is currently 2 meters tall so this tower that sits on top of the tree is 2 meters tall currently and if he or I fee adds to it at about zero point 2 meters a month so I guess he or she I don't know if he won't let's just say he is built is continuously building this tower on this continuously growing tree which is fascinating all right the function a of M returns the trees height in meters and months from now fascinating the function B of M returns the towers height in meters and months from now so this is the tree side a of M is a tree sight B of M is the towers height find the formula of the two functions so a of M so they tell us the tree is currently 5 meters tall so it's going to be 5 meters tall right at the start and then every month it is growing by 0.1 meters so it's going to be 5 plus 0.1 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 0 months which is right now where 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 all right now let's think about the tower so the formula for B of M so the tower is currently 2 meters tall so it's currently 2 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 unit's here we're just assuming that 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 all right the function C of M returns the vertical distance between the ground and the top end of the tower it makes sense that would be from the bottom of the tree to the top of the tower right the formula C of M in terms of a and a of M and B of n 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 V of M plus B of n that's what C of M is going to be and then they say write the formula of C of M in terms of M well we just need to add these two functions if we add five plus 0.1 m 2 2 plus 0.2 m that's going to be so we could add 5 plus 2 and we're going to get 7 plus and if I have 0.1 m and I add another point to M that's going to be 0.3 m 0 0.3 m and we are done we got it right