Question

Rank these functions according to their growth, from slowest growing (at the top) to fastest growing (at the bottom).

Answer 1

To rank functions based on their growth rates, we can look at their equations or examine the behavior of their graphs. The slowest growing function is the linear function, followed by the quadratic function, and the fastest growing function is the exponential function.

Step-by-step explanation:

The functions can be ranked based on their growth rates. The slowest growing function will have the smallest rate of change, while the fastest growing function will have the largest rate of change. To rank the functions, we can look at their equations or examine the behavior of their graphs.

1. Linear function: A linear function has a constant rate of change, so it grows at a steady pace. It has a growth rate of 1, which means it grows by a fixed amount over a given interval. Therefore, it is the slowest growing function.
2. Quadratic function: A quadratic function has a growth rate that increases as the input values increase. The growth rate is proportional to the square of the input values. Therefore, it grows faster than a linear function but slower than an exponential function.
3. Exponential function: An exponential function has a growth rate that increases exponentially as the input values increase. The growth rate is proportional to the function value itself. Therefore, it grows faster than both linear and quadratic functions and is the fastest growing function.

Therefore, the functions can be ranked from slowest growing to fastest growing as follows: Linear function, Quadratic function, Exponential function.