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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 number , 000, prompting a debate on how to control their growth and avoid koalas dying of starvation.1 assuming exponential growth, find the (continuous) rate of growth of the koala population between 1996 and 2005. Round your answer to one decimal place.

Respuesta :

Answer: The continuous growth rate of koalas is 18.7%.

We use the formula for continuous growth to find the rate of growth. The formula is:

[tex]Population_{2007} = Population_{1996}*e^{rt}[/tex]

Substituting the values we get,

[tex]26000 = 5000*2.71828^{9r}[/tex]

[tex]\frac{26000}{5000} = 2.71828^{9r}[/tex]

[tex]5.4 = 2.71828^{9r}[/tex]

We can solve this equation further by taking the normal log of both sides of the equation.

[tex]ln5.4 = 9r * ln2.71828[/tex]

[tex]1.686398954=9r*0.999999327[/tex]

[tex]1.686398954=8.999993946r[/tex]

[tex]\frac{1.686398954}{8.999993946} =r[/tex]

[tex]0.187377788 = r[/tex]

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