Question

The population of rabbits on an island is growing exponentially. In the year 1990, the population of rabbits was 190, and by 1994 the population had grown to 280. Predict the population of rabbits in the year 2001, to the nearest whole number.

Answer 1

in this problem

the equation is of the form

y=a(b)^x

where

a is the initial value

a=190

x=0 -----> is the year 1990

so

y=190(b)^x

For year 1994 -----------> x=1994-1990=4 years

y=280

substitute

280=190(b^4)

solve for b

b^4=280/190

b=1.10

therefore

y=190(1.10)^x

In the year 2001

x=2001-1990=11 years

substitute

y=190(1.10)^11

y=542 rabbits