A dehumidifier is used to reduce the moisture in a basement. The level of moisture reported on the display panel when the dehumidifier is turned on is 70%. The percent moisture, P(t), at time t is recorded for different times t in the table. $$\begin{array} { l l l l l l l }
T & 0 & 2 & 6 & 15 & 20 & 30 \
P ( t ) & 70 & 67 & 60 & 53 & 51 & 50
\end{array}$$ Estimate P'(20).
A)-0.20% per minute
B)-0.10% per minute
C)0.10% per minute
D)0.20% per minute
E)0.40% per minute

Question

A dehumidifier is used to reduce the moisture in a basement. The level of moisture reported on the display panel when the dehumidifier is turned on is 70%. The percent moisture, P(t), at time t is recorded for different times t in the table. $$\begin{array} { l l l l l l l } 
T & 0 & 2 & 6 & 15 & 20 & 30 \
P ( t ) & 70 & 67 & 60 & 53 & 51 & 50
\end{array}$$ Estimate P'(20).
A)-0.20% per minute
B)-0.10% per minute
C)0.10% per minute
D)0.20% per minute
E)0.40% per minute

Quizplus · Accepted Answer

P'(20) can be estimated using the average rate of change around t = 20. Using the values at t = 15 and t = 30, we calculate: $\frac{P(30) - P(15)}{30 - 15} = \frac{50 - 53}{15} = \frac{-3}{15} = -0.20$. However, this calculation error leads to the choice of -0.20% per minute, which is not listed as an option. The correct approach for a closer estimate around t = 20, using the values at t = 15 and t = 30, should yield a different rate, focusing on a narrower interval for a more accurate derivative approximation at t = 20. Given the options and recognizing a mistake in the initial calculation explanation, the correct estimation method involves using points closer to t = 20, if available, to find a more precise rate of change. However, without closer points, the calculation should correctly interpret the rate of change between the given times, suggesting a reevaluation of the calculation or the interpretation of the options provided. The correct answer, considering the options and the typical method for estimating derivatives at a point, involves recognizing the average rate of change as an approximation of the derivative.

A Dehumidifier Is Used to Reduce the Moisture in a Basement