Question

question 5: maya has been tracking how the value of a cell phone (in hundreds of dollars) changes over time (in years) since it was first purchased. the scatter plot below shows the data she collected. which model best represents the data? a. $y = 10(0.9)^{x}$ b. $y = 10(0.5)^{x}$ c. $y = - 1.2x + 10$ d. $y = - 0.5x + 7$

Explanation:

Step1: Analyze the type of function

The scatter - plot shows a linear trend (not an exponential trend as the points seem to follow a straight - line pattern more closely than a curved exponential pattern). So we can eliminate options A and B (which are exponential functions of the form \(y = a\cdot b^{x}\)).

Step2: Check the slope and y - intercept of the linear functions

For a linear function \(y=mx + b\), where \(m\) is the slope and \(b\) is the y - intercept.

• For option C: \(y=-1.2x + 10\), when \(x = 0\), \(y = 10\) (y - intercept). The slope \(m=-1.2\).
• For option D: \(y=-0.5x + 7\), when \(x = 0\), \(y = 7\) (y - intercept). The slope \(m=-0.5\).

We can also use the "rise over run" concept. If we assume two points \((x_1,y_1)\) and \((x_2,y_2)\) from the scatter - plot. Let's assume \((x_1 = 0,y_1\approx10)\) and \((x_2=5,y_2\approx4)\)
The slope \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{4 - 10}{5-0}=\frac{-6}{5}=-1.2\)

Answer:

C. \(y=-1.2x + 10\)