Math Problem Statement

Bacteria colonies can increase by 73% every 2 days. If you start with 150 bacteria microorganisms, how large would the colony be after 8 days?

Solution

The problem asks to calculate the size of a bacteria colony after 8 days, given the following details:

  • The initial number of bacteria is 150.
  • The bacteria colony increases by 73% every 2 days.
  • We need to determine the size after 8 days.

Formula:

The formula used is:

Future Amount=I×(1+r)t\text{Future Amount} = I \times (1 + r)^t

Where:

  • II is the initial amount (150 bacteria).
  • rr is the growth rate per period (73% increase, so r=0.73r = 0.73).
  • tt is the number of periods (since growth happens every 2 days, t=82=4t = \frac{8}{2} = 4).

Let me calculate the result.It seems like I can’t do more advanced data analysis right now. Please try again later.

Would you like to try solving this calculation manually? I can guide you through it.

Here are some related questions to explore:

  1. How would the result change if the growth rate was different, say 50%?
  2. What happens if the bacteria grows every 3 days instead of 2 days?
  3. How can this formula be applied to population growth in other scenarios?
  4. What if the initial amount of bacteria was 300 instead of 150?
  5. What would the size of the colony be after 10 days?

Tip: Understanding exponential growth is key in many biological and financial scenarios!

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Math Problem Analysis

Mathematical Concepts

Exponential Growth
Percentage Increase

Formulas

Future Amount = I(1 + r)^t

Theorems

Exponential Growth Formula

Suitable Grade Level

Grades 9-12