The arithmetic sequence function is f(n) = 56 - 8(n-1). The movie earns $16 million in week 6 and $176 million overall, considering the provided data.
a. To determine the function representing the arithmetic sequence, we need to find the common difference (d) between consecutive terms. The common difference is the change in the money earned each week.
From the given coordinates:
Going from (1, 56) to (2, 48), the difference is -8.
Going from (2, 48) to (3, 40), the difference is also -8.
Going from (3, 40) to (4, 32), the difference is once again -8.
Therefore, the common difference (d) is -8. We can now use this information to write the function:
f(n) = a + (n-1)d
Where:
a is the initial term, which is the money earned in the first week.
n is the week number.
d is the common difference.
Let's use the point (1, 56) to find a:
56 = a + (1-1)(-8)
a = 56
So, the function is:
f(n) = 56 - 8(n-1)
b. To find the week when the movie earns $16 million, we set f(n) to 16 and solve for n:
16 = 56 - 8(n-1)
n - 1 = 5
n = 6
So, the movie earns $16 million in week 6.
c. To find the overall money earned, we need to sum the terms of the arithmetic sequence. The sum is given by the formula:
Sn = n/2[2a + (n-1)d]
Using n = 4 (the number of weeks) and the found values of a and d:
S4 = 4/2[2(56) + (4-1)(-8)]
S4 = 2[112 - 24]
S4 = 2(88)
S4 = 176
Therefore, the movie earns $176 million overall.
The question probable may be:
The amount of money a movie earns each week after its release can be approximated by the sequence shown in the graph. a. Write a function that represents the arithmetic sequence. f(n)=□ b. In what week does the movie earn $16 million? The movie earns $16 million week in □ . c. How much money does the movie earn overall? The movie earns $□ million
The coordinates of the graph are ( 4 , 32) ( 2, 48) (3 , 40) ( 1, 56)