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The population of rabbits on an island is growing exponentially. In the year 2005, the population of rabbits was 6900, and by 2012 the population had grown to 13500.

Predict the population of rabbits in the year 2015, to the nearest whole number.

2 Answers

1 vote

Answer:

To predict the population of rabbits in the year 2015, we can use the exponential growth formula:

P(t) = P0 * e^(kt),

where:

P(t) is the population at time t,

P0 is the initial population,

e is the base of the natural logarithm (approximately 2.71828),

k is the growth rate constant.

Given that the population in 2005 (t = 0) was 6900, we have:

P(0) = 6900.

We're also given that by 2012 (t = 7), the population had grown to 13500, so we have:

P(7) = 13500.

We can use these two data points to solve for the growth rate constant, k.

Substituting the values into the formula:

13500 = 6900 * e^(k * 7).

Dividing both sides by 6900:

e^(k * 7) = 13500 / 6900.

Taking the natural logarithm of both sides:

k * 7 = ln(13500 / 6900).

Dividing both sides by 7:

k = ln(13500 / 6900) / 7.

Now that we have the value of k, we can predict the population in 2015 (t = 10) using the formula:

P(10) = P0 * e^(k * 10).

Substituting the values:

P(10) = 6900 * e^((ln(13500 / 6900) / 7) * 10).

Calculating this expression, we find:

P(10) ≈ 15711.

Therefore, the population of rabbits in the year 2015 is predicted to be approximately 15711 to the nearest whole number.

Hope that helps!

User Blearn
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Explanation:

I hope this answer is helpful ):

The population of rabbits on an island is growing exponentially. In the year 2005, the-example-1
User Weijian
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