Question

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.

Answer 1

Tyler is right. I agree with him

Explanation:

Exponential Function

The given exponential function is

`f(x)=5^x`

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

`f(x+1)=5^(x+1)=5\cdot 5^(x)`

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

`f(x+1/10)=5^(x+1/10)=5^(1/10)\cdot 5^(x)`

Note that the factor for this increment of x is

`5^(1/10)=\sqrt[10]{5}`

We can see that Tyler is absolutely right