Question

The total movie attendance in a country was 1.16 billion people in 1990 and 1.40 billion in 2008. Assume that the pattern in movie attendance is linear function of time. (Need to answer questions a-d for this question - pic attached)

Answer 1

a)

In order to find a function M(t), first let's identify two ordered pairs that are solutions to the equation.

From the given information, we have the ordered pairs (1990, 1.16) and (2008, 1.4).

Using these ordered pairs, let's find the slope-intercept form of a linear equation (y = mx + b)

`\begin{gathered} m=(y_2-y_1)/(x_2-x_1) \\ m=(1.4-1.16)/(2008-1990)=(0.24)/(18)=0.01333 \\ \\ y=mx+b \\ 1.16=1990\cdot0.01333+b \\ b=-25.3667 \\ \\ y=0.01333x-25.3667 \end{gathered}`

So the equation is M = 0.01333t - 25.3667

The independent variable represents the year (correct option: first one)

b)

The slope represents the change in M over the change in t, that is, it represents the change in attendance over a year (correct option: first one)

c)

For t = 2015, we have:

`\begin{gathered} M=0.01333\cdot2015-25.3667 \\ M=26.86-25.37 \\ M=1.49 \end{gathered}`

d)

For M = 1.5, we have:

`\begin{gathered} 1.5=0.01333\cdot t-25.3667 \\ 0.01333t=26.8667 \\ t=2015.5 \end{gathered}`