This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Here's the solution to the problem: Step 1: Determine the initial number of bacteria and the time duration. The initial number of bacteria at 8:00 AM is given as 2^3. The time duration from 8:00 AM to 8:00 PM is 12 hours. Step 2: Calculate the number of doublings. Since the bacteria double every hour, over 12 hours, the bacteria will double 12 times. This means the initial number will be multiplied by 2^12. Step 3: Express the total number of bacteria using powers of 2. To find the total number of bacteria at 8:00 PM, multiply the initial number by the doubling factor: Total bacteria = Initial bacteria × 2^number of hours Total bacteria = 2^3 × 2^12 Using the exponent rule a^m × a^n = a^m+n: Total bacteria = 2^3+12 Total bacteria = 2^15 Step 4: Calculate the actual number of bacteria. 2^15 = 32768 The number of bacteria at 8:00 PM, expressed using powers of 2, is 2^15. The actual number of bacteria is 32768. That's 2 down. 3 left today — send the next one.