# Solving Systems of Equations Approximately Project

04.03 Solving Systems of Equations Approximately Project. A lake has a native population of 1,000 frogs. The native frog population increases at a rate of 200 frogs per year. A new species of 10 frogs migrates to the lake. This new species’ population increases at a rate of 50% per year. When will the two populations equal each other? Select to reveal each frog population’s growth model.

A system of equations can be created with the two functions to determine when the populations will have the same population output value, y.

y = 200x + 1,000

y = 10(1.5^{x})

To determine when the populations will be equal, set the equations equal to each other, and solve for x.

200x + 1,000 = 10(1.5^{x})

This equation is a little more challenging to solve by algebraic methods. In this lesson, you will solve systems of equations like the one above approximately by effectively using technology and tables.

Student completes the table with the correct values.

Student finds the solution to the equation.

Student uses the graph to justify the statement.

Student uses the graph to determine the approximate year that the two ad revenues were equal.

Student interprets and analyzes the data in a table.

Student determines the approximate solution.

Student determines the approximate solution.

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