Question

# The temperature, in degrees Celsius (°C), of the water in a pond is a differentiable function W of time t. The

table above shows the water temperature as recorded every 3 days over a 15-day period. (a) Use data from the table to find an approximation for W (12). Show the computations that lead to your answer. Indicate units of measure. (b) Approximate the average temperature, in degrees Celsius, of the water over the time interval 0 15 t days by using a trapezoidal approximation with subintervals of length t 3 days. (c) A student proposes the function P, given by ( / 3) ( ) 20 10 t P t te , as a model for the temperature of the water in the pond at time t, where t is measured in days and P t( ) is measured in degrees Celsius. Find P(12). Using appropriate units, explain the meaning of your answer in terms of water temperature. t (days) W t( ) (°C) 0 3 6 9 12 15 20 31 28 24 22 21