Exam 6: Differential Equations

A calf that weighs 75 pounds at birth gains weight at the rate where w is weight in pounds and t is time in years. If the animal is sold when its weight reaches 900 pounds, find the time of sale using the model . Round your answer to two decimal places. ​

Solve the differential equation. ​ ​

The initial investment in a savings account in which interest is compounded continuously is $768. If the time required to double the amount is years, what is the amount after 13 years? Round your answer to the nearest cent. ​

Find the particular solution of the differential equation that satisfies the boundary condition . ​

We modeled populations of aphids and ladybugs with a Lotka-Volterra system. Suppose we modify those equations as follows: ​ , ​ . ​ Find the population equilibrium point. ​

Suppose an eight-pound object is dropped from a height of 5,000 feet, where the air resistance is proportional to the velocity. Write the velocity as a function of time if its velocity after 4 seconds is approximately -50 feet per second. Use a graphing utility or a computer algebra system. Round numerical answers in your answer to four places. ​

Solve the differential equation. ​ ​

Which of the following is a solution of the differential equation ? ​

A calf that weighs 50 pounds at birth gains weight at the rate where w is weight in pounds and t is time in years. What is the maximum weight of the animal if one uses the model ? ​

Find the particular solution of the differential equation that satisfies the boundary condition . ​

A 200-gallon tank is full of a solution containing 25 pounds of concentrate. Starting at time distilled water is added to the tank at a rate of 20 gallons per minute, and the well-stirred solution is withdrawn at the same rate. Find the time at which the amount of concentrate in the tank reaches 15 pounds. Round your answer to one decimal place.

Find the function passing through the point with the first derivative . ​

Solve the Bernoulli differential equation .

Solve the first order linear differential equation. ​ ​

Solve the differential equation . ​

Sketch the slope field for the differential equation and use the slope field to sketch the solution satisfying the condition . ​

Find the logistic equation that satisfies the following differential equation and initial condition. ​ , ​

Find the time (in years) necessary for 1,000 to double if it is invested at a rate 6% compounded continuously. Round your answer to two decimal places. ​

Select from the choices below the slope field for the differential equation. ​ ​

Select from the choices below the slope field for the differential equation. ​ ​