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

$$ m = \frac{99.5 - 100}{1 - 0} = -0.5 $$

Identify the y-intercept

$$ b = 100 \quad \text{at} \quad x = 0 $$

Formulate the linear equation

$$ y = -0.5x + 100 $$

Answer:

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