Question

Which situation can be modeled by a linear function? A) The cost of living in the city doubles every 10 years. B )The employees at a local hardware store earn a $2-per-hour wage increase every year they work for the store. C) Each bacteria in the petri dish divides in half every five seconds. D) A rumor spreads when you tell 5 of your friends, who each tell 5 more of their friends, and each of those friends tell 5 more of their friends, etc.

Answer 1

The condition for linear functions is that we have a constant rate of change of y versus x.

A) In this case, the rate of variation is exponential and not constant, so it is not linear.

B) In this case we can model the wage increase y versus the years of work x as a linear function, as y is proportional to x. Then, the rate of change of y versus x is constant (is equal to 2 $/year).

For example, with x=0 years working, it corresponds a y=0 wage increase.

When x=1, it corresponds a y=2 wage increase.

When x=2, it corresponds a y=4 wage increase.

When x=n, it correspond a y=2n wage increase.

Then, the function that relates wage increase and years working is y=2x, that is a linear function.

C) The same as case A, where the rate of variation is not constant but exponential.

D) This case is also exponential and the rate of variation is not constant.

Answer: Option B.