Question

a lake near susans house is predicted to lose water every day because of a drought. the table shows the estimated water depth in feet, \\(y\\), after \\(x\\) days of drought.

choose the function that represents the data.

\\(y = -0.5x + 100\\)
\\(y = -x^{0.5} + 100\\)
\\(y = -0.5x^2 + 100\\)
\\(y = -\frac{x}{0.5} + 100\\)

Explanation:

Calculate the rate of change

$$ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{99.5 - 100}{1 - 0} = -0.5 $$

Identify the y-intercept

$$ b = y(0) = 100 $$

Formulate the linear equation

$$ y = mx + b \implies y = -0.5x + 100 $$

Answer:

• (A) \(y = -0.5x + 100\) (Correct answer)
• (B) \(y = -x^{0.5} + 100\)
• (C) \(y = -0.5x^2 + 100\)
• (D) \(y = -\frac{x}{0.5} + 100\)