Chapter 10: Q32. (page 528)

Determine whether the function $y = 0.2 {(5)}^{- x}$ represents exponential growth or decay.

Short Answer

Expert verified

The given function $y = 0.2 {(5)}^{- x}$ representsexponential decay.

Step by step solution

Step 1. Write down the given information.

The given function is $y = 0.2 {(5)}^{- x}$ .

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;

$\begin{array}{l} y = 0.2 {(5)}^{- x} .... (Given) \\ y = 0.2 {(5^{- 1})}^{x} \\ y = 0.2 {(\frac{1}{5})}^{x} \end{array}$

Now, from the concept stated above it can be interpreted that the function $y = 0.2 {(\frac{1}{5})}^{x}$ will represent exponential decay because the base (b) of the function $y = 0.2 {(\frac{1}{5})}^{x}$ is such that $0 < b < 1$ . Hence, the given function $y = 0.2 {(5)}^{- x}$ represents exponential decay.

Step 4. Conclusion.

The given function $y = 0.2 {(5)}^{- x}$ represents exponential decay.

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Determine whether the function $y = 0.2 {(5)}^{- x}$ 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.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Calculus

Applied Mathematics

Pure Maths

Geometry

Decision Maths

Study anywhere. Anytime. Across all devices.

Determine whether the function y=0.25-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.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Calculus

Applied Mathematics

Pure Maths

Geometry

Decision Maths

Study anywhere. Anytime. Across all devices.

Determine whether the function $y = 0.2 {(5)}^{- x}$ represents exponential growth or decay.