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The population of rabbits on an island is growing exponentially. In the year 1990, the
population of rabbits was 6200, and by 1994 the population had grown to 10800.
Predict the population of rabbits in the year 1998, to the nearest whole number.

Answer :

Answer:

The approximate population in 1998 is 18,769

Step-by-step explanation:

Here, we want to predict the population

If it follows an exponential pattern, then we have the equation as follows

y = I( 1 + r)^n

Where y is the present year population

I is the initial population which is the population in 1990

r is the growth rate

n is the number of years after 1990

So for 1994, we have

10,800 = 6200(1 + r)^4

divide through by 6,200

That will be

1.74 = (1 + r)^4

we can have this as follows;

ln 1.74 = 4ln (1 + r)

0.554 = 4ln (1+ r)

0.554/4 = ln (1 + r)

1+ r = 1.1485

r = 1.1485 - 1

r = 0.1485

So for 1998, we have

y = 6200(1 + 0.1485)^8

y = 6200(1.1485)^8

y = 18,769

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