Join the IDNLearn.com community and start getting the answers you need today. Our platform provides detailed and accurate responses from experts, helping you navigate any topic with confidence.
Sagot :
To identify the type of function represented by [tex]\( f(x) = 2\left(\frac{1}{2}\right)^x \)[/tex], let's analyze its form step by step.
1. Understanding the Function's Form:
The given function [tex]\( f(x) = 2\left(\frac{1}{2}\right)^x \)[/tex] is of the form [tex]\( f(x) = a \cdot b^x \)[/tex], where [tex]\( a \)[/tex] and [tex]\( b \)[/tex] are constants.
2. Identifying the Constants:
In this function, [tex]\( a = 2 \)[/tex] and [tex]\( b = \frac{1}{2} \)[/tex].
3. Property of the Base [tex]\( b \)[/tex]:
- For exponential functions, [tex]\( b \)[/tex] (the base) determines the behavior of the function.
- If [tex]\( b > 1 \)[/tex], the function represents exponential growth.
- If [tex]\( 0 < b < 1 \)[/tex], the function represents exponential decay.
- In this case, [tex]\( b = \frac{1}{2} \)[/tex], which is less than 1 but greater than 0.
4. Conclusion about the Type of Function:
- Since [tex]\( \frac{1}{2} \)[/tex] (which is [tex]\( b \)[/tex]) is between 0 and 1, the function [tex]\( f(x) = 2\left(\frac{1}{2}\right)^x \)[/tex] represents exponential decay.
Therefore, the type of function represented by [tex]\( f(x) = 2\left(\frac{1}{2}\right)^x \)[/tex] is Exponential decay, corresponding to option B.
1. Understanding the Function's Form:
The given function [tex]\( f(x) = 2\left(\frac{1}{2}\right)^x \)[/tex] is of the form [tex]\( f(x) = a \cdot b^x \)[/tex], where [tex]\( a \)[/tex] and [tex]\( b \)[/tex] are constants.
2. Identifying the Constants:
In this function, [tex]\( a = 2 \)[/tex] and [tex]\( b = \frac{1}{2} \)[/tex].
3. Property of the Base [tex]\( b \)[/tex]:
- For exponential functions, [tex]\( b \)[/tex] (the base) determines the behavior of the function.
- If [tex]\( b > 1 \)[/tex], the function represents exponential growth.
- If [tex]\( 0 < b < 1 \)[/tex], the function represents exponential decay.
- In this case, [tex]\( b = \frac{1}{2} \)[/tex], which is less than 1 but greater than 0.
4. Conclusion about the Type of Function:
- Since [tex]\( \frac{1}{2} \)[/tex] (which is [tex]\( b \)[/tex]) is between 0 and 1, the function [tex]\( f(x) = 2\left(\frac{1}{2}\right)^x \)[/tex] represents exponential decay.
Therefore, the type of function represented by [tex]\( f(x) = 2\left(\frac{1}{2}\right)^x \)[/tex] is Exponential decay, corresponding to option B.
Your participation means a lot to us. Keep sharing information and solutions. This community grows thanks to the amazing contributions from members like you. For dependable and accurate answers, visit IDNLearn.com. Thanks for visiting, and see you next time for more helpful information.