Video Transcript
Given an initial value π₯ sub zero, we can iterate a function using a recursive formula. π₯ sub π equals π of π₯ sub π minus one. Find π₯ sub three, given the function π of π₯ equals three π₯ minus two with an initial value of π₯ sub zero equals two.
So our initial value is π₯ sub zero equals two. So if we would like to find π₯ sub one, then we need to plug in one for π. And one minus one is zero. So we need to plug in π of π₯ sub zero, meaning we plug in π₯ sub zero into our function. So instead of three π₯ minus two, we need three times π₯ sub zero minus two.
And we know what π₯ sub zero is; itβs equal to two. So we have three times two minus two. Three times two is six, and six minus two is four. So π₯ sub one is equal to four. So now to find π₯ sub two, we plug in two for π. So we will evaluate π of π₯ sub one. And we can replace π₯ sub one with four. Three times four is 12, and 12 minus two is 10. So π₯ sub two is equal to 10.
So lastly, to find π₯ sub three, what we were asked to find, we plug in three for π, evaluate π of π₯ sub two, replace π₯ sub two with 10. And three times 10 is 30, and 30 minus two is 28. So π₯ sub three is equal to 28.
