Linear function of slope

Question

The linear function f(x) = 46.9 + 62.2 models the number of smartphones sold in some country, f(x), in millions, x years after 2006. Find the slope of the model. Then describe what this means in terms of the rate of change of the dependent variable per unit change in the independent variable.

Answer 1

f(x) = 46.9x + 62.2

the slope = 46.9 = the derivative of f(x) = f'(x)

for every one unit increase in x, the independent variable, there is a 46.9 increase in f(x), the dependent variable

each year after 2006 there is an increase of 46.9 million more phones sold

the rate of change is a constant