Video: Calculating a Predicted Value Using an Exponential Regression Model

Given the exponential regression model 𝑦 = 4 × 1.2^𝑥, determine the value of 𝑦 when 𝑥 is equal to 0.

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Video Transcript

Given the exponential regression model 𝑦 equals four multiplied by 1.2 to the power of 𝑥, determine the value of 𝑦 when 𝑥 is equal to zero.

Now, the first thing to consider is what is an exponential regression model. Well, this is a model for a set of data that can take the form of an exponential function, for example, the function that we have here. And contrarily to what it might sound like, an exponential regression model can take the form of an exponential function that is increasing or decreasing. Now to solve this problem, what we need to do is work out what the value of our model is going to be when 𝑥 is equal to zero. So what is the value of 𝑦 when 𝑥 is equal to zero?

So to calculate that, what we’re gonna have is 𝑦 is equal to four multiplied by 1.2 to the power of zero. And that’s because our 𝑥-value is zero. Well, in fact, we know that anything to the power of zero is just gonna be equal to one. So we can rewrite it as 𝑦 is equal to four multiplied by one. And that’s because 1.2 as we’ve already said if it’s to the power of zero, it’s just gonna be equal to one.

So therefore, we can say the value of 𝑦 when 𝑥 is equal to zero if 𝑦 is equal to four multiplied by 1.2 to the power of 𝑥 is going to be four.

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