Question

The population of rabbits on an island is growing exponentially. In the year 1992, the population of rabbits was 810, and by 1997 the population had grown to 930. Predict the population of rabbits in the year 2004, to the nearest whole number.

Answer 1

Answer:

1128

Step-by-step explanation:

Let the exponential function for the population of rabbits on the island is given by  

$P = a(b)^{t}$......... (1), where t is the number of years.

Now, if we count the time in years from 1992, then the initial value of the function i.e. population in the year 1992 is, a = 820.

So, the equation becomes $P = 820(b)^{t}$ ........ (2)

Now, in the year 1997 i.e. at t = 5 years, P = 930.

Hence, from equation (2) we get,  

$930 = 810(b)^{5}$

⇒ b = 1.028

Hence, the final equation is $P = 810(1.028)^{t}$ ........ (3)

Now, in 2004, t = (2004 - 1992) = 12 years, the population will be {From equation (3)}

$P = 810(1.028)^{12} = 1128.44$ ≈ 1128 (Answer)