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A lake ecosystem has a fish population that doubles every year. If there are ini

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Question: A lake ecosystem has a fish population that doubles every year. If there are initially 50 fish, how many fish will there be after 4 years?

Options:

  1. 200
  2. 400
  3. 800
  4. 1600

Correct Answer: 1600

Solution: 

50 * 2^4 = 50 * 16 = 800 fish.

A lake ecosystem has a fish population that doubles every year. If there are ini

Practice Questions

Q1
A lake ecosystem has a fish population that doubles every year. If there are initially 50 fish, how many fish will there be after 4 years?
  1. 200
  2. 400
  3. 800
  4. 1600

Questions & Step-by-Step Solutions

A lake ecosystem has a fish population that doubles every year. If there are initially 50 fish, how many fish will there be after 4 years?
  • Step 1: Start with the initial number of fish, which is 50.
  • Step 2: Understand that the fish population doubles every year.
  • Step 3: Calculate how many times the population will double in 4 years. It will double 4 times.
  • Step 4: Use the formula for doubling: Initial number of fish multiplied by 2 raised to the power of the number of years. This is written as 50 * 2^4.
  • Step 5: Calculate 2^4, which means 2 multiplied by itself 4 times: 2 * 2 * 2 * 2 = 16.
  • Step 6: Now multiply the initial number of fish (50) by the result from Step 5 (16): 50 * 16.
  • Step 7: Calculate 50 * 16, which equals 800.
  • Step 8: Therefore, after 4 years, there will be 800 fish in the lake.
  • Exponential Growth – The concept of exponential growth is tested, where a quantity increases by a constant factor over equal intervals of time.
  • Doubling Time – Understanding how populations can double over time and the mathematical representation of this growth.
  • Basic Arithmetic Operations – The question requires basic multiplication and exponentiation to arrive at the final answer.
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