Key Features of Exponential Functions

Exponential Function

Subject | Subject

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2. Identify the growth or decay factor

3. Determine if it is growth or decay

   1. If the factor is less than 1, it is decay.

   2. If the factor is greater than 1, it is growth.

4. ​Solve for r.​

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​A stock is purchased for $35. Its value increases by 50% each year.

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Model this scenario using an exponential equation.

​increasing by 50% means that this is an exponential growth function

​2 to the power of any number will never be zero. It is get infinitely close to zero, but never actually zero. This is why you have a curved bracket, because zero is not included by everything greater than it is.

​There is not an x-intercept, only a y-intercept

​This end behavior notation means:

"as x approaches negative infinity, y approaches 0 and as x approaches infinity, y approaches infinity"​

​The "left" and "right" sides of the graph extend infinitely with no breaks or asymptotes in the middle.

​The graph never touches or crosses the x-axis. It only crosses the y-axis at 5.

​The graph approaches the x-axis infinitely but will never touch or cross.

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y = ? is the equation for horizontal lines​

​The graph goes up to infinity on the left which is where x approaches negative infinity.

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The graph approaches 0 on the right which is where x approaches infinity.​

​Try Example 1 on page 140 in your workbook by yourself. Check your work on the next slide.