Question

The amount of money a movie earns each week after it’s release can be approximated by the sequence shown in the graph. a. Write a function that represents the arithmetic sequence.

Answer 1

A amount of money is modeled by a linear function.

The function that represents the arithmetic sequence is: $\mathbf{y = -20x + 120}$

From the graph, we have the following points:

$\mathbf{(x_1,y_1) = (1,100)}$ --- amount earned (million dollars) in the first week

$\mathbf{Rate = 20\ less}$ ---- ($20 million less each additional week)

A linear function is represented as:

$\mathbf{y= mx + b}$

Where:

• m represents rate
• b represents the y-intercept

So, we have:

$\mathbf{100= -20 \times 1 + b}$

$\mathbf{100= -20 + b}$

Add 20 to both sides

$\mathbf{120 = b}$

So, we have:

$\mathbf{b = 120}$

Substitute values for m and b in $\mathbf{y= mx + b}$

$\mathbf{y = -20x + 120}$

Hence, the function that represents the arithmetic sequence is: $\mathbf{y = -20x + 120}$

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