Question 9 Identifying The Characteristics of Exponential...

Question 9 Identifying The Characteristics of Exponential Functions Complete the table below for each exponential function. Use Interval Notation to define the Domain and Range. Write intercepts as ordered pairs. If an answer Does Not Exist, write DNE. $y = 1000(0.8)^x$ $y = 100(1.35)^x$ $y = 800(3)^x$ Initial Value(a) Base (b) Domain Range Horizontal Intercept Vertical Intercept as a point Horizontal Asymptote Left to Right Behavior Select an answer Select an answer Select an answer Question Help: Video Message instructor Submit Question

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00:01 In this problem, we want to talk about several different factors that are part of exponential equations.

00:08 So first, just as a quick review, when we look at an exponential equation, we see it in the form y equals a times b to the power of x.

00:19 A is going to represent our initial value.

00:24 B is going to represent our rate of our growth or decay factor, which we can also call our base.

00:36 And then x is simply going to be our exponent.

00:43 It's the independent value.

00:48 So the good news is for all of these given exponential functions, the domain, the range, the horizontal asymptote, and the horizontal intercept are all the same.

01:00 For the domain, it's going to be all real numbers, which you can also enter as negative infinity to positive infinity.

01:12 For the range, it's going to be all y values that are greater than zero, which you can also write as zero to infinity.

01:23 And that happens because the horizontal asymptote will be at y is equal to zero.

01:30 And the horizontal intercept is that there is none.

01:34 No horizontal intercept for exponential equations unless there's been some type of transformation where we translate it up or down.

01:44 Or specifically down.

01:47 All right, so let's check out the initial value for each one of these.

01:52 So we stated that the initial value is the a value.

01:55 So looking at each function, the initial value here would be 600...

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