1. **State the problem:** We start with an initial bacterial count of 698. The bacteria double every 38 minutes. We want to find the bacterial count after 4 hours. 2. **Formula used:** The bacterial growth can be modeled by the formula for exponential growth: $$N = N_0 \times 2^{\frac{t}{d}}$$ where: - $N$ is the final bacterial count, - $N_0$ is the initial bacterial count, - $t$ is the total time elapsed, - $d$ is the doubling time. 3. **Convert time units:** - Total time $t = 4$ hours = $4 \times 60 = 240$ minutes. - Doubling time $d = 38$ minutes. 4. **Calculate the number of doubling periods:** $$\frac{t}{d} = \frac{240}{38} \approx 6.3158$$ 5. **Calculate the final count:** $$N = 698 \times 2^{6.3158}$$ 6. **Evaluate $2^{6.3158}$:** $$2^{6} = 64$$ $$2^{0.3158} \approx 2^{0.3} = 1.231$$ (approximate) So, $$2^{6.3158} \approx 64 \times 1.246 = 79.74$$ (more precise) 7. **Multiply to find final count:** $$N \approx 698 \times 79.74 = 55658.52$$ 8. **Final answer:** The bacterial count after 4 hours is approximately **55659** bacteria.