Certainly! Here's the transcription suitable for an educational website: --- **5. Consider the equations:** \[ f(x) = A \left(1 + \frac{r}{n}\right)^{nx} \] \[ g(x) = A \cdot e^{rx} \] For \( x = 1 \) (a one-year investment) and \( A = 1 \) (a $1 investment), we have: **Simplified:** \[ f(1) = \left(1 + \frac{r}{n}\right)^n \] and \[ g(1) = e^r \] \[ f(1) = 1 \left(1 + \frac{r}{n}\right)^{n \cdot 1} \] and \[ g(1) = 1 \cdot e^{r \cdot 1} \] These equations demonstrate the comparison between compound interest over discrete periods versus continuous compounding. ---

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