Question

The number of McDonald's restaurants worldwide in 2014 was 36.258. In 2009, there were 32,737 McDonald's restau- rants worldwide. Let y be the number of McDonald's res- taurants in the year, where r = O represents the year 2009 (Source: McDonald's Corporation) a. Write a linear equation that models the growth in the number of McDonald's restaurants worldwide in terms of the year x. [Hinr. The line must pass through the points (0.32.737) and (5.30,258).]b. use this equation to predict the number of McDonald's restaurants worldwide in 2016.

Answer 1

Answer:

a) y = 704.2x + 32737

b) There are 37,666 McDonald's restaurants in 2016

Explanations:

The equation of a line passing through the points (x₁, y₁) and (x₂, y₂) is given as:

$\begin{gathered} y-y_1=m(x-x_1) \\ \text{where m is the slope, and is given by the formula: } \\ \text{m = }\frac{y_2-y_1}{x_2-x_1} \end{gathered}$

For the line passing through the points (0, 32737) and (5, 36258)

x₁ = 0, y₁ = 32737, x₂ = 5, y₂ = 36258

Substituting the values into the equations above:

$\begin{gathered} \text{m = }\frac{36258-32737}{5-0} \\ \text{m = }\frac{3521}{5} \\ m\text{ = }704.2 \\ y\text{ - 32737 = 704.2}(x\text{ - 0)} \\ y\text{ - 32737 = 7}04.2x \\ y\text{ = 7}04.2x\text{ + 32737} \\ \end{gathered}$

b) In 2016, x = 7

substitute x = 7 into the equation

$\begin{gathered} y\text{ = 704.2(7) + 32737} \\ y\text{ = }4929.4+32737 \\ y\text{ = }37666.4 \end{gathered}$

There are 37,666 McDonald's restaurants in 2016