Chapter 5: Q. 89 (page 285)

Find an exponential function with horizontal asymptote $y = 2$ whose graph contains the points $(0, 3)$ and $(1, 5)$ .

Short Answer

Expert verified

The exponential function is $y = 3^{x} + 2$ .

Step by step solution

Step 1. Use the given information.

Consider the given horizontal asymptote $y = 2$ .

The two points on the exponential function are $(0, 3)$ and $(1, 5)$ .

If the horizontal asymptote is $y = 0$ , then the exponential function is $y = a^{x}$ .

If the horizontal asymptote is $y = 2$ , then the exponential function is $y = a^{x} + 2$ .

Step 2. Finding exponential function.

On the point $(1, 5)$ , the exponential function is

$5 = a^{1} + 2 5 = a + 2 a = 5 - 2 a = 3$

So the exponential function is $y = 3^{x} + 2$ .

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Find an exponential function with horizontal asymptote $y = 2$ whose graph contains the points $(0, 3)$ and $(1, 5)$ .

Short Answer

Step by step solution

Step 1. Use the given information.

Step 2. Finding exponential function.

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Find an exponential function with horizontal asymptote y=2whose graph contains the points (0,3)and (1,5).

Short Answer

Step by step solution

Step 1. Use the given information.

Step 2. Finding exponential function.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

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Geometry

Study anywhere. Anytime. Across all devices.

Find an exponential function with horizontal asymptote $y = 2$ whose graph contains the points $(0, 3)$ and $(1, 5)$ .