How does f(x) = 6x change over the interval x = 3 to x = 4? a) ƒ(x) increases by 6 b) ƒ(x) decreases by 6 c) ƒ(x) increases by a factor of 6 d) ƒ(x) decreases by a factor of 6

f(x) increases by a factor of 6

Step-by-step explanation:

each time you input 6 and get 18 and then so on and so on... You're increasing not just "by 6" but a FACTOR.

f(3) = 63

f(4) = 64

f(4)

f(3)

=  

64

63

= 64−3 = 61 = 6

The value of ƒ(x) increases from 216 to 1296 over the interval from x = 3 to x = 4.This is an increase by a factor of 6.

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We can extract the points (3, 21) and (6, 12) from the graph.

First we are going to find the slope of the line passing through those points. To do it, we are using the slope formula:

where

is the slope of the line

are the coordinates of the first point

are the coordinates of the second point

Our first point is (3, 21) and our second point is (6, 12), so let's replace the values

Now, to find the equation of the line in point, slope, we are using the point-slope formula:

where

is the slope of the line

are the coordinates of the first point.

Since we have the slope, let's replace the values:

Next, to find the equation in slope-intercept form, we just need to solve our point-slope equation for :

Answer

Equation of the line in point-slope form:

Equation of the line in slope-intercept form:

The time that initially took Scoot  to deliver his packages is the time it took him to deliver the packages in his first day of work. In the hist day of word, zero days has passed since he begin working, so .

It initially took Scoot 30 minutes to deliver his packages.

Now, since the slope of our line is negative 3, Scott's delivery time decreases 3 minutes per day.

Answer

It initially took Scoot 30 minutes to deliver his packages.

Scott's delivery time decreases 3 minutes per day.