Greg made pudding every weekend. the more times he made pudding, the more practice he gained. the time he took to make the same amount of pudding every week decreased with practice. the function below shows the number of hours f(x) greg took to make pudding after he had made it x times: f(x) = 2(0.8)x which graph best represents the function?

Here,  the number of hours ∝ the number of times he did practice

And, this relation is described by the function,

Where,  x is the number of times

f(x) is the number of hours.

The above function f(x) is an exponential function.

Having the y-intercept = (0,2)

But it does not have x-intercept.

End Behaviour:

Since 0.8 < 1

Therefore, the end behaviour of the function f(x) is,

As ,

And, as ,

Thus, from the above information we can plot the graph of the given function. (shown below)

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be