Question

In 1998 there were 1509 daily newspapers in the country. By 2003​, there were only 1454 daily newspapers.

Answer 1

Answer:

The number of daily newspapers in 2000 is estimated in 1487

Step-by-step explanation:

Modeling Functions

Real-world situations are often modeled with mathematic functions. Functions allow making predictions and analysis to better understand and manage those situations

a. In our example, we know that in 1998 there were 1509 daily newspapers in the country. It gives us a starting point (0,1509), where the first coordinate is the years after 1998 and the second is the number of daily newspapers. The second point comes from the next data: by 2003 (5 years after 1998), there were 1454 daily newspapers. The new point is (5,1454).

b. Knowing the relationship between years after 1998 and the numbers of daily newspapers is linear, we can construct the function by using both points. The equation of a line, given the points (a,b) and (c,d) is

$\displaystyle y-b=\frac{d-b}{c-a}(x-a)$

Where y is the number of daily newspapers and x is the number of years after 1998. Using the given points, we have

$\displaystyle y-1509=\frac{1454-1509}{5-0}(x-0)$

$\displaystyle y-1509=-11(x-0)$

$\displaystyle y-1509=-11x$

$y=1509-11x$

c. We can use the above relationship to estimate the number of daily newspapers in 2000. For this year, x=2, thus

$y=1509-11(2)=1487$

The number of daily newspapers in 2000 is estimated in 1487