Question

The population of rabbits on an island is growing exponentially. In the year 1994, the population of rabbits was 9600, and by 2000 the population had grown to 18400. Predict the population of rabbits in the year 2009, to the nearest whole number.

Answer 1

Answer:

49243

Step-by-step explanation:

Given that the population of rabbits on an island is growing exponentially.

Let the population, $P=P_0e^{bt}$

where, $P_0$ and b are constants, t=(Current year -1994) is the time in years from 1994.

In 1994, t=0, the population of rabbit, P=9600, so

$9600=P_0e^{b\times 0}$

So, $P_0=9600$

and in 2000, t=2000-1994=6 years and population of the rabbit, P=18400

$18400=9600 \times e^{b\times 6} \\\\\frac{18400}{9600}=e^{b\times 6}$

$\ln(23/12}=6b$

$b = \frac{\ln{1.92}}{6}$

b=0.109

On putting the value of P_0 and b, the population of the rabbit after t years from 1994 is

$P=9600 \times e^{0.109\times t}$

In 2009, t= 2009-1994=15 years,

So, the population of the rabbit in 2009

$P=9600 \times e^{0.109\times 15}=49243$

Hence, the population of the rabbit in 2009 is 49243.