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Example 4

The population of a country is growing at the rate of one million people per year, while gasoline consumption is decreasing by one billion gallons per year. Find the rate of change of the per capita gasoline consumption when the population is 30 million and total gasoline consumption is 15 billion gallons per year.

By the per capita gasoline consumption we mean the total consumption divided by the population.

Step 1

t = time

x = population

y = gasoline consumption

z = per capita gasoline consumption.

Step 2

At t = t0,

dx/dt = 1 million = 106

dy/dt = -1 billion = - 109

z = y/x.

Step 3

03_continuous_functions-31.gif

Step 4

At t = t0, we are given

x = 30 million = 30 × 106.

y = 15 billion = 15 × 109.

Thus

03_continuous_functions-32.gif

The per capita gasoline consumption is decreasing at the annual rate of 50 gallons per person.

Home Continuous Functions Related Rates Examples Example 4

Last Update: 2006-11-15