Question

Consider, in 2010, there was only one movie produced by Marvel Studios(Iron Man 2). In 2018, there were three (Black Panther, Avengers: Infinity War, and Ant-Man and the Wasp).
a) Find a linear model that shows how many MCU films are made each year (use xx to be years since 2010) using the data above.
b) With the model found in (a), how many MCU films should release in 2020?

Answer 1

Answer:

The answer is below

Explanation:

a) A linear model is represented in the form y = mx + c, where y is the dependent variable, x is the independent variable, m is the rate of change and c is the value of y at x = 0.

Since x = years since 2010, let y = number of movies produced

In 2010 (x = 0), y = 1, this can be represented as (0, 1)

In 2018 (x = 8), y = 3, it can be represented as (8, 3)

Hence, with the points (0,1) and (8, 3) using the formula:

$y-1=\frac{3-1}{8-0}(x-0)\\ \\y-1=\frac{1}{4}x\\\\y=\frac{1}{4}x+1$

b) In 2020 (x = 10), the number of films that would be released is:

$y=\frac{1}{4}x+1\\ \\y=\frac{1}{4}(10)+1\\ \\y=2.5+1\\\\y=3.5\\\\y=3$

3 movies would be released