Exponential Regression Form Recall

00:00 4 marks

Given the exponential model \(y = ab^x\), where \(a\) and \(b\) are constants, state the conditions on \(b\) under which the function represents exponential growth or decay. Additionally, explain the meaning of the parameters \(a\) and \(b\) in the context of this model.

Hint Hint

Hint

Consider the value of \(b\) to determine growth or decay. Remember what \(y\) represents when \(x = 0\).

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Complete Answer

Exponential growth occurs when \(b > 1\) and exponential decay occurs when \(0 < b < 1\). In the model \(y = ab^x\), \(a\) represents the initial value (when \(x=0\)), and \(b\) is the growth/decay factor, indicating the multiplicative change in \(y\) for each unit increase in \(x\).

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