Question

The population of rabbits on an island is growing exponentially. In the year 1991, the population of rabbits was 9100, and by 1998 the population had grown to 18000. Predict the population of rabbits in the year 2006, to the nearest whole number.

Answer 1

Answer:

$39,223\ rabbits$

Step-by-step explanation:

we know that

The equation of a exponential growth function is given by

$y=a(1+r)^x$

where

y is the population of rabbits

x is the number of years since 1991

a is the initial value

r is the rate of change

we have

$a=9,100$

substitute

$y=9,100(1+r)^x$

For the year 1998

the number of years is equal to

x=1998-1991=7 years

so

we have the ordered pair (7,18,000)

substitute in the exponential equation and solve for r

$18,000=9,100(1+r)^7$

$(18,000/9,100)=(1+r)^7$

elevated both sides to 1/7

$(1+r)=1.1023$

$r=0.1023$

therefore

$y=9,100(1+0.1023)^x$

$y=9,100(1.1023)^x$

Predict the population of rabbits in the year 2006

Find the value of x

x=2006-1991=15 years

substitute the value of x in the equation

$y=9,100(1.1023)^{15}$

$y=39,223\ rabbits$