In 1980 the population of alligators in a particular region was estimated to be 1700. In 2005 the population had grown to an estimated 7000.
Using the Malthusian law for population growth, estimate the alligator population in this region in the year 2020.

The Malthusian law for population growth have the folowing form:

the population of alligators in

where is the initial population size , r is the rate of growth and t is time.

By substracting 1980 from t we could say that our is 1700 (the population of alligators in 1980):

and that let us with:

Now we can solve for the 2005 population of 7000 alligator:

By knowing the definition of exponential we can solve:

now we can estimate by replacing t with 2020

So the approximate population in 2020 is 16364 alligators in that region.

step-by-step explanation:

this can be solved first with pythagorean theorem, which tells us to square both legs of the triangle and sum it. this will be equal to the square of the hypotenuse.

the hypotenuse is the side "opposite" the 90 degree angle, which is x.

so we can write using pythagorean theorem,

simplifying:

to further simplify this radical, we need to use the property  

thus