Question

1. connecting to real life the table shows the numbers (in millions) of active accounts for two social media websites over the past five years. assuming this trend continues, how many active accounts will website b have when website a has 280 million active accounts? justify your answer. (see example 2.)

Explanation:

To solve this, we first need to determine the linear relationship between the number of active accounts of Website A (\(x\)) and Website B (\(y\)) using the given data points. Let's list the data points:

\(x\) (Website A)	\(y\) (Website B)
306	215
300	235
299	236
293	253

Step 1: Calculate the slope (\(m\))

We can use two points to calculate the slope. Let's take \((x_1, y_1) = (312, 188)\) and \((x_2, y_2) = (293, 253)\). The slope formula is:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Substituting the values:
\[
m = \frac{253 - 188}{293 - 312} = \frac{65}{-19} \approx -3.421
\]

Step 2: Find the equation of the line

Using the point-slope form \(y - y_1 = m(x - x_1)\) with \((x_1, y_1) = (312, 188)\):
\[
y - 188 = -3.421(x - 312)
\]
Simplify to slope-intercept form (\(y = mx + b\)):
\[
y = -3.421x + (3.421 \times 312) + 188
\]
Calculate \(3.421 \times 312 \approx 1067.35\):
\[
y = -3.421x + 1067.35 + 188
\]
\[
y = -3.421x + 1255.35
\]

Step 3: Predict \(y\) when \(x = 280\)

Substitute \(x = 280\) into the equation:
\[
y = -3.421(280) + 1255.35
\]
Calculate \(-3.421 \times 280 \approx -957.88\):
\[
y = -957.88 + 1255.35 \approx 297.47
\]

Justification

We assumed a linear relationship between the active accounts of the two websites. By calculating the slope and finding the linear equation, we can predict the number of active accounts for Website B when Website A has 280 million. The linear model fits the trend of the data (decreasing \(x\) corresponds to increasing \(y\), suggesting a negative linear relationship).

Answer:

Approximately \(\boldsymbol{297}\) million active accounts (rounded to the nearest whole number).