1. **State the problem:** We have a bacteria colony starting with 1,000 bacteria. The number of bacteria after $t$ hours is given by the formula: $$A = 1000 \times 35.6^{\frac{t}{120}}$$ We need to find the number of bacteria after 48 hours and round to the nearest thousand. 2. **Understand the formula:** - $A$ is the number of bacteria after $t$ hours. - The base number 35.6 is raised to the power of $\frac{t}{120}$, which means the bacteria grow exponentially but at a rate scaled by $\frac{t}{120}$. 3. **Plug in $t=48$ hours:** $$A = 1000 \times 35.6^{\frac{48}{120}}$$ Simplify the exponent: $$\frac{48}{120} = 0.4$$ So, $$A = 1000 \times 35.6^{0.4}$$ 4. **Calculate $35.6^{0.4}$:** Using a calculator or logarithms, $$35.6^{0.4} \approx 4.57$$ 5. **Calculate $A$:** $$A = 1000 \times 4.57 = 4570$$ 6. **Round to the nearest thousand:** $$4570 \approx 5000$$ **Final answer:** After 48 hours, there will be approximately **5000** bacteria in the colony.