3. in order to enter the state fair, there is
an admission cost. each game is $3.
steven went to the state fair, played
4 games and spent a total of $20 on
admission and games. assume the
relationship is linear. find and interpret
the rate of change and the initial value.

C = 8 + 3x

The rate of change in the above equation is 3 dollars per game and it interpret the cost per game.

The initial value in the above equation is 8 dollars, which interpret the entry fee that every one person has to pay to enter the fair.

Step-by-step explanation:

Let the admission cost of the fair is $x and each game is $3.

Now, Steven went to the state fair, played  4 games and spent a total of $20 on  admission and games.

So, we can write 20 = x + 4 × 3 {As the relation is linear}

⇒ x = $8

Therefore, the admission cost in the fair is $8.

Therefore, the equation that models the situation is  

C = 8 + 3x (1)

Where C is the total cost and x is the number of games played.

So, the rate of change in equation (1) is 3 dollars per game and it interprets the cost per game.

Again, the initial value in equation (1) is 8 dollars, which interprets the entry fee that each person has to pay to enter the fair. (Answer)

3030 ur welcome

step-by-step explanation:

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