Chapter 10: Q31. (page 528)

Determine whether the function $y = 30^{- x}$ represents exponential growth or decay.

Short Answer

Expert verified

The given function $y = 30^{- x}$ representsexponential decay.

Step by step solution

Step 1. Write down the given information.

The given function is $y = 30^{- x}$ .

Step 2. Concept used.

The exponential function is of the form $y = a b^{x}$ represents exponential growth if the base $b > 1$ and exponential decay if the base $0 < b < 1$ for all $a > 0$ .

Step 3. Explanation.

The given function can be re-written as;

$\begin{array}{l} y = 30^{- x} \\ y = {(30^{- 1})}^{x} \\ y = {(\frac{1}{30})}^{x} \end{array}$

From the concept stated above it can be interpreted that the function $y = {(\frac{1}{30})}^{x}$ will represent exponential decay because the base (b) of the function $y = {(\frac{1}{30})}^{x}$ is such that $0 < b < 1$ . Hence, the given function $y = 30^{- x}$ represents exponential decay.

Step 4. Conclusion.

The given function $y = 30^{- x}$ represents exponential decay.

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Determine whether the function $y = 30^{- x}$ represents exponential growth or decay.

Short Answer

Step by step solution

Step 1. Write down the given information.

Step 2. Concept used.

Step 3. Explanation.

Step 4. Conclusion.

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Determine whether the function y=30-xrepresents exponential growth or decay.

Short Answer

Step by step solution

Step 1. Write down the given information.

Step 2. Concept used.

Step 3. Explanation.

Step 4. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Pure Maths

Discrete Mathematics

Decision Maths

Applied Mathematics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Determine whether the function $y = 30^{- x}$ represents exponential growth or decay.