Question

I'm confused can someone please explain to me how to do this?​

Answer 1

The function displayed in the table is best described as an Exponential Decay Function.

Explanation:

First, the main difference between a linear and an exponential function is the shape of its graph, as well as the presence of either a constant ratio or a constant rate of change.

Linear functions are functions with a base function of
`f(x)=mx+b`, which has a constant rate of change (
`m`), and the shape of its graph will be a straight line.

Exponential functions on the other hand use the base function
`f(x)=a^x`, where
`a` is the constant ratio of the function, and its graph is curved and has a horizontal asymptote that the graph will approach but never touch as it either increases or decreases to positive or negative infinity respectively.

The function in the problem gives you four points that are on its graph: (-2, 540), (-1, 270), (0, 135), and (1, 67.5). Using these points, you can determine whether it is a linear or exponential function. You can tell that when the x-value increases by 1, the f(x) value is divided by 2, or multiplied by
`(1)/(2)`. Since there is a constant ratio instead of a constant rate of change in the function, you would know that the function in the table is an exponential function. Since the function is also constantly decreasing, the function would be best described as an Exponential Decay Function.

Have a great day! Feel free to let me know if you have any more questions :)