Applications of Separable Differentials

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Applications of Separable Differentials What do you believe to be the fastest growing city in America? How about fastest growing Metro Area?

The Fastest Growing City in America The population of New York City is increasing at a rate of 1.9% per year. The instantaneous rate of change can be related to its population at any given moment. The population as of now is 8,336,697. Find an equation to estimate the population of NYC for any year. When will the population double?

The Fastest Growing Metropolitan Area in the Country The population of Houston, Texas is increasing at a rate of 2.74% per year. The instantaneous rate of change can be related to its population at any given moment. The population as of now is 6,490,180. Find an equation to estimate the population of Houston for any year When will the population double?

Applications of Separable Differentials You are driving in your car on a dark country road. You run over a nail. As air begins to leak out of your tire, the rate of change of the air pressure inside the tire is directly proportional to that pressure. Write a differential equation if the pressure is 35 psi and decreasing at 0.28 psi per minute. (Hint: find percentage decrease of .28 psi compared to 35 psi and use as the rate). Solve for y Assuming the car is safe to drive at a psi of 12 or higher, how long will the car be safe to drive?

Applications of Separable Differentials