1. the population of the small town of parks in 2000 was estimated to be 3,901 people with an annual rate of decrease of about 1.8%. at this rate, what is the estimated population in 2013.

Given that the population of the small town of Parks in 2000 was estimated to be 3,901 people with an annual rate of decrease of about 1.8%. Now we have to find about what is the estimated population in 2013. So we can use decay formula:

where P is the initial population so P=3901

r= rate of decrease = 1.8%= 0.018

t=number of years  since 2000 = 13

Now plug these values to find the value of A

A=3080.52892878

Hence final answer is approx 3080.

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: