# Question Video: Calculating a Predicted Value Using an Exponential Regression Model Mathematics

Given the exponential regression model π¦ = 3.1 Γ 0.5^π₯, estimate the value of π¦ when π₯ is equal to 4.

01:23

### 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 weβve 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 weβre going to do is substitute π₯ into our equation or our regression model.

So therefore, what weβre 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 thatβs 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 itβs 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.