Tyler says that the function f(x)=5^x is exponential and so it grows by equal factors over equal intervals. He says that factor must be 10root of 5 for an interval of 1/10 because ten of those intervals makes an interval of length 1. Do you agree with Tyler? Explain your reasoning.

Tyler is right. I agree with him

Step-by-step explanation:

Exponential Function

The given exponential function is

Tyler says it grows by equal factors over equal intervals which is true. We'll show why below.

If x grows by 1 unit, the growth of the function will be

Note that the function grew by a factor of 5, as Tyler said. But what happens if x grows by 1/10?

Note that the factor for this increment of x is

We can see that Tyler is absolutely right

in geometry, parallel lines are lines in a plane which do not meet; that is, two lines in a plane that do not intersect or touch each other at any point are said to be parallel. by extension, a line and a plane, or two planes, in three-dimensional euclidean space that do not share a point are said to be parallel.