1. **State the problem:** We have a bacterial culture starting with 1000 bacteria, modeled by the formula $$N = 1000 \times 2^{\frac{t}{5}}$$ where $N$ is the number of bacteria after $t$ hours. 2. **Explain the parameters:** - The number 1000 is the initial amount of bacteria at time $t=0$. - The base 2 represents the growth factor, meaning the bacteria double every 5 hours. - The denominator 5 in the exponent indicates the doubling time in hours. 3. **Calculate bacteria after 1 day (24 hours):** Use the formula with $t=24$: $$N = 1000 \times 2^{\frac{24}{5}}$$ 4. **Simplify the exponent:** $$\frac{24}{5} = 4.8$$ 5. **Evaluate the power:** $$2^{4.8} = 2^{4 + 0.8} = 2^4 \times 2^{0.8} = 16 \times 2^{0.8}$$ 6. **Calculate $2^{0.8}$ approximately:** $$2^{0.8} \approx 1.741$$ 7. **Multiply to find $N$:** $$N = 1000 \times 16 \times 1.741 = 1000 \times 27.856 = 27856$$ **Final answer:** After 1 day, there are approximately **27856 bacteria** present.