A sunflower is 3 inches tall at week 0 and grows 2 inches each week. Does the function `f(n) = f(n - 1) + 2 where f(0) = 3` represent the height, f(n), in "n" weeks?

Question

calculusxy · Answer

@mathstudent55 @mathmale @agent0smith

calculusxy · Answer

The answer key actually says that it does. But I don't know why.

faiqraees · Answer

It should be this
General formula for arithmetric progression = a +(n-1)d
$$\large\rm F_n = 3+ 2n$$

agent0smith · Answer

The given formula should work. f(n-1) represents the height last week, and adding 2 matches the description.

faiqraees · Answer

@agent0smith
What's the value of f(n-1) when n = 0 and how's f(0)=3

agent0smith · Answer

f(0) = 3 is a given. You don't use the function to find it. The next week would be n=1. The formula is correct.

faiqraees · Answer

How's the formula satisfying f(0) = 3

agent0smith · Answer

Did you not read what I just wrote? f(0) = 3 is a given initial value.

faiqraees · Answer

like mine satisfies 
f(0) = 3 +2n
f(0) = 3+2(0)
f(0) = 3

agent0smith · Answer

f(1) = f(0) + 2
f(2) = f(1) + 2

and so on.

It's a recursive formula. 

It is correct. It's equivalent to yours.