The constant proportionality between the number of markers and the number of pencils in our room is eight over three. there are 304 markers in the art room. how many pencils are in the art room

There are 114 pencils in the art room

Solution:

Given, The constant proportionality between the number of markers and the number of pencils in our room is eight over three.  

There are 304 markers in the art room.  

We have to find how many pencils are in the art room.

Now, from the above formula.

Hence, there are 114 pencils in the art room

6e14 is the answer.

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt