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Wanahton purified a portion of water with 900 grams of contaminants. Each hour, a third of the contaminants was filtered out.

Let g(n) be the amount of contaminants (in grams) that remained by the beginning of the nth hour. g is a sequence, what kind of sequence is it, arithmetic or geometric? Then, write an explicit formula for the sequence, g(n)=?

Step-by-step explanation:

If wanahton purified a portion of water with 900 grams of contaminants and each hour, a third of the contaminants was filtered out then the amount of grams filtered out first hour will be 1/3 of 900grams = 300grams.

The amount filtered out in the second hour will be 1/3 of 300grams = 100grams.

Given the initial amount of contaminant = 900g

Contaminant after 1st hour = 300g

contaminant after 2nd hour = 100g and so on

It is seen that the amount of contaminant keep reducing by one third each hour. The sequence formed will be 900, 300, 100... which is a GEOMETRIC SEQUENCE because they are reducing by the same factor each term which is 1/3.

Given the geometric sequence 900, 300, 100...the nth term of the sequence is expressed as shown;

g(n) =

r is the common ratio = =  

n is the umber of terms

a is the first term which serves as the initial value of the contaminant= 900

Substituting the values given to get the explicit formula for the sequence we have;

g(n) =

The amount of contaminants (in grams) that remained by the beginning of the nth hour is

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