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

.19875994384

step-by-step explanation:

1699/ 8548

c. y = 1/4 x + 5

step-by-step explanation:

first, put the equation of the line on the graph into slope-intercept form

(y = mx + b):   y = -4x + 8

second, a perpendicular line has to have "an opposite/reciprocal slope" to the original slope. so, find the "m" value in your original equation (it's -4, right? )

original slope: m = -4   perpendicular slope: change the sign to its opposite and find the reciprocal ("flip" the number)

new slope is now positive (b/c the original slope was negative 4), and it's 1/4 (not the original slope of 4 or 4/1)