Welcome to Westonci.ca, your go-to destination for finding answers to all your questions. Join our expert community today! Join our Q&A platform to get precise answers from experts in diverse fields and enhance your understanding. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.
Sagot :
To determine which of the given functions represents an exponential growth function, we need to analyze the base [tex]\( b \)[/tex] of the exponential term [tex]\( b^x \)[/tex]. An exponential growth function is characterized by a base [tex]\( b \)[/tex] where [tex]\( b > 1 \)[/tex].
Let's examine each function step by step:
1. [tex]\( f(x) = 6(0.25)^x \)[/tex]:
- The base of the exponential term here is [tex]\( 0.25 \)[/tex].
- Since [tex]\( 0.25 < 1 \)[/tex], this function represents exponential decay, not growth.
2. [tex]\( f(x) = 0.25(5.25)^x \)[/tex]:
- The base of the exponential term here is [tex]\( 5.25 \)[/tex].
- Since [tex]\( 5.25 > 1 \)[/tex], this function represents exponential growth.
3. [tex]\( f(x) = -4.25^x \)[/tex]:
- The base of the exponential term here is [tex]\( -4.25 \)[/tex].
- Generally, negative bases for exponents are not considered typical exponential growth functions, as the function can have complex and alternating behavior depending on whether [tex]\( x \)[/tex] is an integer or not.
4. [tex]\( f(x) = (-1.25)^x \)[/tex]:
- The base of the exponential term here is [tex]\( -1.25 \)[/tex].
- Similar to the previous case, negative bases are not treated as generic exponential growth functions due to potential complex and alternating behavior.
Among the given options, the function [tex]\( f(x) = 0.25(5.25)^x \)[/tex] is the one that represents exponential growth because the base [tex]\( 5.25 \)[/tex] is greater than [tex]\( 1 \)[/tex].
Therefore, the correct answer is:
Option 2: [tex]\( f(x) = 0.25(5.25)^x \)[/tex]
Let's examine each function step by step:
1. [tex]\( f(x) = 6(0.25)^x \)[/tex]:
- The base of the exponential term here is [tex]\( 0.25 \)[/tex].
- Since [tex]\( 0.25 < 1 \)[/tex], this function represents exponential decay, not growth.
2. [tex]\( f(x) = 0.25(5.25)^x \)[/tex]:
- The base of the exponential term here is [tex]\( 5.25 \)[/tex].
- Since [tex]\( 5.25 > 1 \)[/tex], this function represents exponential growth.
3. [tex]\( f(x) = -4.25^x \)[/tex]:
- The base of the exponential term here is [tex]\( -4.25 \)[/tex].
- Generally, negative bases for exponents are not considered typical exponential growth functions, as the function can have complex and alternating behavior depending on whether [tex]\( x \)[/tex] is an integer or not.
4. [tex]\( f(x) = (-1.25)^x \)[/tex]:
- The base of the exponential term here is [tex]\( -1.25 \)[/tex].
- Similar to the previous case, negative bases are not treated as generic exponential growth functions due to potential complex and alternating behavior.
Among the given options, the function [tex]\( f(x) = 0.25(5.25)^x \)[/tex] is the one that represents exponential growth because the base [tex]\( 5.25 \)[/tex] is greater than [tex]\( 1 \)[/tex].
Therefore, the correct answer is:
Option 2: [tex]\( f(x) = 0.25(5.25)^x \)[/tex]
We hope our answers were helpful. Return anytime for more information and answers to any other questions you may have. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.