6.4: Comparing Quadratic and Exponential Functions Activ 4. Here are two functions: p(x)
q(x) = 34.
6x2 and
Investigate the output of p and q for different values
of x. For large enough values of x, one function will
have a greater value than the other. Which function will
have a greater value as x increases?
Support your answer with tables, graphs, or other
representations
NOTE: Graph the two equations using Desmos on the
next slide.
Х
p(x)
9(x)

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

answer: $1794

step-by-step explanation:

add the numbers under frequency to find the total number:

5 + 8 +7 + 4 + 0 +1 = 25

the answer is 25.