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November 7th, 2017, 04:31 AM   #1
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exponential growth

In 1923, koalas were introduced to Kangaroo Island. In 1996, the population was 5000. By 2005, the population had grown to 27000, prompting a debate on how to control their growth and avoid koalas dying of starvation. Assuming exponential growth, find the continuous rate of growth of the koala population between 1996 and 2005. Find a formula for the population as a function of the number of years since 1996, and estimate the population in the year 2020.

My answer:
1996 to 2005 = 9 years
Exponential growth model: Q(t) = (Qo)(e^kt)
Q(t) = 5000e^kt
27,000 = 5000e^k9
5.4 = e^k9
ln(5.4) = 9k
k=0.1874

Q(t) = 5000e^0.1874t
Q(24) = 5000e^0.1874(24)
= 449,007 is the population in year 2020.

As above, my answer addresses the question 'Find a formula for the population as a function of the number of years since 1996, and estimate the population in the year 2020.'

However, I'm not sure how to answer the question 'Assuming exponential growth, find the continuous rate of growth of the koala population between 1996 and 2005.'

If anyone can help, I would greatly appreciate it!

Last edited by skipjack; November 7th, 2017 at 09:51 PM.
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November 7th, 2017, 05:37 AM   #2
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Not sure what you're doing...
P = Present value (5000)
F = Future value (27000)
n = number of years (9)
r = rate (?)

Formula: r = (F / P)^(1 / n) - 1

r = (27000 / 5000)^(1 / 9) - 1 = ~.2061

Somehow you got ~.1874
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November 7th, 2017, 02:54 PM   #3
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In the textbook, they give very brief solutions. For this question, they wrote:

k=[ln(27000/5000)]/9 = 0.1874
P(t)=5000e^(0.1874t)
P(24)=449,007

From what I learnt in class, k = elimination rate constant

But I'm not sure how to answer the 'Assuming exponential growth, find the continuous rate of growth of the koala population between 1996 and 2005' part of the question.

Last edited by skipjack; November 7th, 2017 at 09:46 PM.
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November 7th, 2017, 03:56 PM   #4
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Quote:
Originally Posted by pianist View Post
From what I learnt in class, k = elimination rate constant
Hmmm....never heard of that...
hopefully someone else has and will come to the rescue!
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