In this lesson, we will learn how to identify, write, evaluate, sketch and analyze natural exponential functions.

Students will be able to

Q1:

Jacob has graphed three exponential functions all in the form 𝑦=𝑎𝑒.

The red graph represents the equation 𝑦=𝑒.

By considering properties of graphical transformations, determine the equation of the blue graph.

By considering properties of graphical transformations, determine the equation of the green graph.

Q2:

The graph below is of the function 𝑓(𝑥)=𝐴1−𝑒 for constants 𝐴 and 𝑘.

Determine, from the information in the graph, what the values of 𝐴 and 𝑘 are. Round the result to three decimal places if necessary.

Q3:

What is the equation, in the form 𝑦=𝐴𝑒, of an exponential function whose graph passes through the points (0,3.62) and (10,4.604)?

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