Question

question
which of the contexts below could not be modeled by a linear function?
answer
a taxi charges a flat fee of $3.50 for pick - up, then an additional fee of $3.75 per mile.
snow was melting at a rate of 2.5 inches per hour.
a population of 450 bacteria quintuples every week.
a music service has a fixed monthly cost and charges $0.15 for each downloaded song.

Explanation:

A linear function has a constant rate of change.

1. The taxi cost has a flat fee plus a constant per-mile charge, so it follows a linear model: $C = 3.50 + 3.75m$ where $m$ is miles.
2. Snow melting at a constant 2.5 inches per hour has a constant rate of change, following a linear model: $S = S_0 - 2.5t$ where $t$ is hours.
3. The music service has a fixed monthly cost plus a constant per-song charge, following a linear model: $C = F + 0.15s$ where $F$ is the fixed cost and $s$ is number of songs.
4. A bacteria population that quintuples (multiplies by 5) every week is exponential, not linear, as its growth rate is proportional to its current size, following the model $P = 450 \times 5^w$ where $w$ is weeks. This does not have a constant rate of change.

Answer:

A population of 450 bacteria quintuples every week.