Question 18 of 18, Step 1 of 1 Bacteria in a bottle are tripling every minute. If the number of bacteria in the bottle at 5:00 p.m. is 1 , how many bacteria are in the bottle at \( 5: 12 \) p.m.? Answer How to enter your answer (opens in new window)

To determine the number of bacteria in the bottle at 5:12 p.m., we start with the fact that the bacteria triple every minute starting from 1 at 5:00 p.m. Here's the step-by-step calculation: 1. **Initial Count at 5:00 p.m.**: 1 bacterium. 2. **Number of Minutes Elapsed**: 12 minutes (from 5:00 p.m. to 5:12 p.m.). 3. **Growth Factor**: The bacteria triple every minute, so the growth factor is \( 3^{12} \). Calculating \( 3^{12} \): \[ 3^1 = 3 \\ 3^2 = 9 \\ 3^3 = 27 \\ 3^4 = 81 \\ 3^5 = 243 \\ 3^6 = 729 \\ 3^7 = 2,187 \\ 3^8 = 6,561 \\ 3^9 = 19,683 \\ 3^{10} = 59,049 \\ 3^{11} = 177,147 \\ 3^{12} = 531,441 \] **Therefore, the number of bacteria at 5:12 p.m. is \( \boxed{531441} \).**