In 1923, koalas were introduced on Kangaroo Island off the coast of Australia. I
ID: 3214886 • Letter: I
Question
In 1923, koalas were introduced on Kangaroo Island off the coast of Australia. In 1996, the population was 5000, By 2005 , the population had grown to 27,000 ,prompting a debate on how to control their growth and avoid koalas dying of starvation1. Assuming exponential growth, find the (continuous) rate of growth of the koala population between 1996 and 2005. Round your answer to one decimal place. The continuous growth rate is %. Find a formula for the population as a function of the number of years since 1996. The formula is P = Estimate the population in the year 2012 using your value of K. Round your answer to the nearest thousand koalas. The population in the year 2012 wi|| be approximately thousand koalas. 1news. yahoo. com/s/afp/australiaanimalskoalas, accessed June 1, 2005.Explanation / Answer
Let's say 1996 is year 0
P(0) = 5000
P(9) = 27000
Say, P(t) = P(0)*exp(r*t), where r is the rate of growth
Solve for k:
P(t)/P(0) = exp(k*t)
ln(P(t)/P(0)) = k*t
k = (1/t)*ln(P(t)/P(0))
Say t = 9, then
k = (1/9)*ln(27000/5000)
k = 18.7%
P(t) = 5000*exp(0.187*t)
2012 is 16 years after 1996, so
P(16) = 5000*exp(0.187*16)
P(16) = 100,000, rounded to the nearest 1000. (Enter 100 in the box, though)