Identify whether the following real-world example should be modeled by a linear,
quadratic, or exponential function.
Type the correct word (linear, quadratic, or exponential) as
your answer.

A. Each ink cartridge purchased for $12.

B. Throwing a ball.

C. The amount of money you earn when you get paid an hourly wage.

D. A bank account balance earning an annual interest rate.

E. Maximizing the area of a rectangular fenced area in a large field.

F. Population growth of a city.

  linear: A, C

  quadratic: B, E

  exponential: D, F

Step-by-step explanation:

Sales and wages are usually modeled by a linear function. The amount earned or paid is proportional to the quantity involved.

Compound interest and population are proportional to the current value, which increases when the amount of growth is added. The model is an exponential one.

Models of ballistic motion are usually simplified to quadratic functions*. Likewise, the area of a rectangle is a quadratic function of its dimensions.

The usual sorts of models used are ...

  A. linear

  B. quadratic

  C. linear

  D. exponential (for compound interest)

  E. quadratic

  F. exponential

* Before the age of computers, the ballistic tables used for aiming artillery were computed using mechanical desk calculators to numerically solve differential equations involving wind speed and direction, air temperature and humidity, and the rotation of the earth. The model was not your simple quadratic function as used in high-school algebra.

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