Consider a pond that initially contains 10 million gal of fresh water. Stream water containing an undesirable chemical flows into the pond at the rate of 5 million gal/yr. and the mixture in the pond flows out through an overflow culvert at the same rate. The concentration y(t) of the incoming water varies periodically with time t, measure in years, according to the expression y(t) = 2+ sin 2t g/gal. a. Write out the differential equation that models this scenario. Include the initial value as well. b. Solve the initial value problem from a. You may use technology to help with the integration. c. Plot this solution for t e (0,20) years. What is happening to this pond as time moves on?

Iron is mixed with an acid in an insulated container. The temperature, T°C, above room temperature, at time t minutes after the metal is added to the acid is given by: a) b) T = 64tet Calculate the rate of change of the temperature 5 minutes after the metal is added. When t = 5 minutes then °C/min. Give your answer to two decimal places, if needed. Calculate the maximum temperature of the mixture. The maximum temperature of the mixture is Give your answer to two decimal places, if needed. °C above room temperature.

11.) Consider the function f(t) = lnt. a.) Calculate the instantaneous rate of change of 1 the function at t = 2 b.) Find the equation of the tangent line at the point where t=3. Leave your answer in terms of the natural logarithm.

for y = + VE Find hp da