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Home > CALC > Chapter 8 > Lesson 8.3.1 > Problem 8-105


Multiple Choice: The population of a city is growing according to the equation . The current population of the city is . Assuming the same pattern of growth, what will be the population be in six years?

Notice that the given equation is a derivative. It gives information about the rate of change of the population. But what we want to know is information about the actual population. How do we undo a derivative?

It is necessary to use implicit integration because the derivative is in terms of time, but time does not appear in the equation.

Separate the sides: 

Integrate both sides.

Combine the constants of integration.

Evaluate the given point to solve for :

Substitute in the value of , then write an equation for .

Use your equation to find Population at years.