Question 1 Suppose 25 E. coli bacteria are introduced into some food as it's being processed, and the bacteria begins tripling every day. How many bacteria are there after one week? bacteria

To determine the number of **E. coli** bacteria after one week (7 days), given that the bacteria triple every day, follow these steps: 1. **Initial Quantity:** - Start with **25** bacteria. 2. **Daily Growth Factor:** - The bacteria **triple** each day, which means each day the number of bacteria is multiplied by **3**. 3. **Calculation Over 7 Days:** - The growth can be represented by the formula: \[ \text{Final Number of Bacteria} = \text{Initial Quantity} \times 3^{\text{number of days}} \] - Plugging in the values: \[ \text{Final Number of Bacteria} = 25 \times 3^7 \] - Calculate \(3^7\): \[ 3^7 = 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 = 2187 \] - Now, multiply by the initial quantity: \[ 25 \times 2187 = 54,675 \] 4. **Conclusion:** - After **7 days**, there will be **54,675 bacteria**. **Final Answer:** After one week, there are 54 675 bacteria.