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**Answer Attempt 1 out of 2**

The population of rabbits on an island is growing exponentially. In the year 2001, the population of rabbits was 940, and by 2006 the population had grown to 2050. Predict the population of rabbits in the year 2009, to the nearest whole number.

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Answer :

Final answer:

To predict the population of rabbits in the year 2009, we can use the exponential growth formula. Using the given data, we find that the predicted population of rabbits in 2009 is approximately 2247 rabbits.


Explanation:

To predict the population of rabbits in the year 2009, we can use the exponential growth formula, which is given by:

P(t) = P0 * ert

Where:

  • P(t) is the population at time t
  • P0 is the initial population
  • r is the continuous growth rate
  • t is the time elapsed

Using the given data, we can substitute P0 = 940, P(t) = 2050, and t = 2006 - 2001 = 5 into the formula. Solving for r:

2050 = 940 * e5r

e5r = 2050/940

e5r = 2.18

Using natural logarithms to undo the exponential function:

5r = ln(2.18)

r = ln(2.18)/5 ≈ 0.1657

Now that we have the growth rate, we can use it to predict the population in 2009:

P(2009) = 940 * e^(0.1657 * (2009 - 2001))

Calculating this, we find that the predicted population of rabbits in 2009 is approximately 2247 rabbits.


Learn more about exponential growth here:

https://brainly.com/question/12490064


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