# Write an exponential function that begins its rapid increase

Questions Eliciting Thinking What is the basic form of an exponential function? Exponential functions are solutions to the simplest types of dynamical systems. Correctly calculates the initial amount and growth factor, but neglects to write the exponential function. If the student wrote a linear function, ask the student to graph the function and compare it to the given graph.

Discuss with the student differences in the rates of increase of the two functions and relate these differences to the forms of the equations.

Examples of Student Work at this Level The student attempts to write a linear function or an exponential expression. Provide opportunities for the student to explore and investigate exponential functions given in context. Encourage the student to relate features of the graph to the parameters in the equation.

Questions Eliciting Thinking What do the values in the equation tell you about the exponential equation and its graph? Questions Eliciting Thinking What does the value you calculated,tell you about this graph?

We can also change the exponential function by including a constant in the exponent. Can you describe them in words? Explain the significance of points whose coordinates are of the form 0, x and 1, x and demonstrate how these points can be used to write the equation.

If the value of b had beenwhat would you know about the equation and its graph? Almost There The student makes a minor error in calculating a parameter or writing the function. Did you write the function? For example, an exponential function arises in simple models of bacteria growth An exponential function can describe growth or decay.

You can see this fact through the above applet. What are the two important parameters of an exponential function? The student does not understand the basic form of an exponential function.Jul 08,  · How to Write an Exponential Function Given a Rate and an Initial Value.

Exponential functions can model the rate of change of many situations, including population growth, radioactive decay, bacterial growth, compound interest, and much %(1). Write an exponential function that begins its rapid increase when 2 = x = 3.

More Write another that begins its rapid increase when 3 ≤ x ≤ 4.

Write a third that begins its rapid increase when 6 ≤ x ≤ 8. What was the impact of industrialization on family life and standards of living Exponential Growth Write an exponential fiction.

Exponential relation, exponent of the base number, exponential graph, exponential growth, exponential decay, domain of an exponential function, range of an exponential function.

Open-Ended Write an exponential function that begins its rapid increase Write a third that begins its rapid increase when 6 Chapter 6 worksheet answers.

Write an exponential function that begins its rapid increase when 2 is less than or equal to x is less than or equal to 3.

write another that begins its rapid increase when 3 is less than or equal to x is less than or equal to 4. Correctly calculates the initial amount and growth factor, but neglects to write the exponential function.

Provide additional opportunities to write exponential functions given their graphs. Writing an Exponential Function From Its Graph worksheet; SOURCE AND ACCESS INFORMATION.

Write an exponential function that begins its rapid increase
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