Question

A website records the number of referrals it received, y, from social media websites over time, x.

time (years) 5 6 7 8
cost ($) 18,984 28,477 42,715 64,072
Note: The number of referrals is rounded to the nearest whole number.

Which type of function would best be used to model this situation? Explain how you arrived at your answer.
short explanation

Answer 1

To determine the best type of function to model the relationship between time and the number of referrals, we can analyze the provided data:

- As time increases (from 5 to 8 years), the cost significantly increases. The costs are not increasing linearly; they grow at an accelerating rate (the difference between consecutive costs is increasing).

Given these characteristics, an exponential function or possibly a quadratic function may be suitable since both types can exhibit rapid growth. However, the increasing rate of growth in the costs suggests that an exponential function may be the most appropriate model. Exponential functions can describe situations where growth accelerates over time (such as the viral spread of referrals on social media).

Thus, an exponential model can be likely derived from this set of data, reflecting the nature of the relationship effectively.