Solve for the variable \( P \) to two decimal places. \( 63,200=\mathrm{Pe}{ }^{0.065(8)} \) \( \mathrm{P}=\square \) (Round to two decimal places as needed.)

To solve for \( P \) in the equation \( 63,200 = \mathrm{Pe}^{0.065(8)} \), we first calculate the exponent: \[ 0.065 \times 8 = 0.52. \] Now, the equation simplifies to: \[ 63,200 = \mathrm{Pe}^{0.52}. \] Next, we can isolate \( P \) by dividing both sides by \( e^{0.52} \): \[ P = \frac{63,200}{e^{0.52}}. \] Calculating \( e^{0.52} \) gives us approximately \( 1.6788 \). Thus, we have: \[ P = \frac{63,200}{1.6788} \approx 37,693.75. \] Therefore, rounding to two decimal places: \( \mathrm{P} = 37,693.75 \)