Question A sample of bacteria is decaying according to the half-life model \( f(t)=N e^{-0.220 t} \), where \( N \) is the initic is time in hours. At \( t=4 \), there are 25 bacteria remaining. What was the initial sample amount? Round your final answer to the nearest whole number. Do not include units.

We start with the decay model \[ f(t) = N e^{-0.220t} \] Given that at \( t=4 \) there are 25 bacteria, we substitute to obtain \[ 25 = N e^{-0.220 \cdot 4}. \] Simplify the exponent: \[ -0.220 \times 4 = -0.88, \] so that \[ 25 = N e^{-0.88}. \] To solve for \( N \), divide both sides by \( e^{-0.88} \): \[ N = \frac{25}{e^{-0.88}} = 25 e^{0.88}. \] Now, calculate \( e^{0.88} \). Using a calculator, \[ e^{0.88} \approx 2.410. \] Thus, \[ N \approx 25 \times 2.410 \approx 60.25. \] Rounding to the nearest whole number gives \[ N \approx 60. \]