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katen-ka-za [31]
3 years ago
10

In 1923, koalas were introduced on kangaroo island off the coast of australia. In 1996, the population was 5000. By 2005, the po

pulation 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.
Business
1 answer:
zzz [600]3 years ago
6 0

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:

Population_{2007} = Population_{1996}*e^{rt}

Substituting the values we get,

26000 = 5000*2.71828^{9r}

\frac{26000}{5000} = 2.71828^{9r}

5.4 = 2.71828^{9r}

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

ln5.4 = 9r * ln2.71828

1.686398954=9r*0.999999327

1.686398954=8.999993946r

\frac{1.686398954}{8.999993946} =r

0.187377788 = r

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The price of one share of such a stock today is $49.86

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The stock's price today under the Dividend discount model can be calculated by discounting the expected future dividends to the present value using an appropriate discount rate. When the dividend growth becomes constant, we calculate the terminal value and discount it back too. The appropriate discount rate is the required rate of return. The worth of one of such stock today is,

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The correct answer is: change more quickly than ever before.

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They are marginal quantities (change made by additional unit) so everything has been taken into account for the deriving of change to surplus.

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