Questions: The temperature of water in a certain lake on a day in October can be determined by using the model y=15.2-0.537x where x is the number of feet down from the surface of the lake and y is the Celsius temperature of the water at that depth. Based on this model, how deep in the lake is the water 4 degrees? Round to the nearest foot. A. 39 ft B. 77 ft C. 36 ft D. 21 ft

Solution Steps

To find the depth at which the water temperature is 4 degrees Celsius, we need to solve the equation \( y = 15.2 - 0.537x \) for \( x \) when \( y = 4 \). This involves rearranging the equation to isolate \( x \) and then calculating the value of \( x \).

We start with the model for the temperature of water in the lake given by the equation: \[ y = 15.2 - 0.537x \] where \( y \) is the temperature in degrees Celsius and \( x \) is the depth in feet.

To find the depth at which the temperature is \( 4 \) degrees Celsius, we substitute \( y = 4 \) into the equation: \[ 4 = 15.2 - 0.537x \]

Rearranging the equation to solve for \( x \): \[ 0.537x = 15.2 - 4 \] \[ 0.537x = 11.2 \] \[ x = \frac{11.2}{0.537} \]

Calculating the value of \( x \): \[ x \approx 20.8566 \] Rounding to the nearest foot gives: \[ x \approx 21 \]

Final Answer