### Video Transcript

Given the exponential regression model π¦ equals 3.1 multiplied by 0.5 to the power of π₯, estimate the value of π¦ when π₯ is equal to four.

So first of all, what we notice is that weβve got a regression model. And what this means is that as our π₯-value increases, the value of π¦ will decrease or regress. So now, what we want to do is work out what the value of π¦ is going to be when π₯ is equal to four. And to do this, what weβre going to do is substitute π₯ into our equation or our regression model.

So therefore, what weβre gonna have is π¦ is equal to 3.1 multiplied by 0.5 to the power of four. And this is gonna be equal to 3.1 multiplied by 0.0625. And thatβs because 0.5 to the power of four is the same as a half to the power of four. Well, a half to the power of four is equal to one over two to the power of four. Two to the power of four is 16. So itβs one over 16, which is 0.0625.

So therefore, given the exponential regression model π¦ equals 3.1 multiplied by 0.5 to the power of π₯, our estimate for the value of π¦ when π₯ is equal to four is 0.19375.