Problem 2. The depth of water at a certain dock varies due to tidal forces. At both 8am and 8pm, the water is at its deepest value of 10 ft. At 2pm, the water is at its shallowest depth of only 4 ft. (a) First, as always, define variables for time and depth of water. For both, be sure to specify units, and for time, be sure to specify the starting time for your variable. (b) Since the depth of the water cycles between high and low tide, we will use a sinusoidal model. Find the period, amplitude, mininimum, maximum, and average values that should be used for this model.

(c) Write down an equation that models the depth of water at time t. (d) Predict the depth of water at 9am.

Problem 3. Suppose population of a certain ant hill doubles every 10 days, and the popu- lation is 1000 ants on May 6. (a) First, as always, define variables for time and population of ants in the ant hill. For both, be sure to specify units, and for time, be sure to specify the starting time for your variable. (b) Use an exponential model to write down an equation that models the population of ants in this ant hill over time. (c) Predict the number of ants in the ant hill on May 31