Math Problem Statement

If a food contains 10 food poisoning bacteria and it is left in conditions that allow each bacterium to divide into two every 10 minutes, how many bacteria will there be on the food item after 1 hour

Solution

The number of bacteria doubles every 10 minutes. This means the growth follows exponential progression.

Step 1: Define the Growth Formula

The formula for bacterial growth is:

N=N0×2nN = N_0 \times 2^n

where:

  • N0=10N_0 = 10 (initial bacteria count),
  • nn is the number of times the bacteria double,
  • NN is the final bacteria count.

Step 2: Determine nn

Since bacteria double every 10 minutes, and we are given a total time of 1 hour (60 minutes):

n=6010=6n = \frac{60}{10} = 6

Step 3: Calculate the Final Number of Bacteria

N=10×26N = 10 \times 2^6

N=10×64N = 10 \times 64

N=640N = 640

Final Answer:

After 1 hour, there will be 640 bacteria on the food item.

Would you like a more detailed explanation of exponential growth?

Related Questions:

  1. What would happen if the bacteria doubled every 5 minutes instead?
  2. How long would it take for the bacteria to reach 10,000?
  3. What is the formula for exponential growth in general?
  4. What factors affect bacterial growth in food?
  5. How can food poisoning be prevented by controlling bacterial growth?

Quick Tip:

To slow bacterial growth, keep food at temperatures below 5°C (41°F) or above 60°C (140°F), as bacteria grow fastest between 5°C and 60°C (the "danger zone").

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Math Problem Analysis

Mathematical Concepts

Exponential Growth
Powers of Two

Formulas

N = N0 × 2^n

Theorems

Exponential Growth Formula

Suitable Grade Level

Grades 7-10