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Can we use Multiple Linear Regression to predict a dependent variable that is growing exponentially with time?

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When you have an exponential shape in $x$, you can transform $x$ by taking logs.

So while a model $y=\beta x + u$ will likely perform badly, a model such as $y=\beta \log(x)+u$ will likely perform better.

However, based on your minimal description of the problem, you cannot expect a really detailed answer.

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