Question

Given a sequence of data in context where the outputs are constantly increasing but the rate of growth is decreasing, which of the following functions would best model the data? Assume the dataset indicates that there are no relative extrema. (1 point)
Responses

a linear function
a linear function

a cubic function
a cubic function

a logarithmic function
a logarithmic function

an absolute value function

Answer 1

Given that the outputs of the sequence are constantly increasing while the rate of growth is decreasing, the appropriate function to model this data would be a **logarithmic function**.

Logarithmic functions increase at a decreasing rate as their input values increase, which aligns with your description of the data.

The other options do not fit the scenario as follows:
- A linear function would have a constant rate of growth, not a decreasing rate.
- A cubic function could exhibit both increasing and decreasing behavior depending on the coefficients and degree, and may possess relative extrema.
- An absolute value function has a V-shape and does not consistently increase without relative extrema.

Therefore, the best choice is:

**a logarithmic function**.