Answered

Westonci.ca is the premier destination for reliable answers to your questions, brought to you by a community of experts. Get immediate and reliable answers to your questions from a community of experienced experts on our platform. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.

Which exponential function has an initial value of 2?

A. [tex]\( f(x) = 2 \cdot 3^x \)[/tex]
B. [tex]\( f(x) = 3 \cdot 2^x \)[/tex]

Sagot :

GinnyAnswer
To determine which exponential function has an initial value of 2, let's evaluate each function at [tex]\( x = 0 \)[/tex].

Given the functions:
1. [tex]\( f(x) = 2 \cdot 3^x \)[/tex]
2. [tex]\( f(x) = 3 \cdot 2^x \)[/tex]

We can evaluate these functions at [tex]\( x = 0 \)[/tex]:

### Evaluating [tex]\( f(x) = 2 \cdot 3^x \)[/tex] at [tex]\( x = 0 \)[/tex]:

[tex]\[ f(0) = 2 \cdot 3^0 \][/tex]
Since any number raised to the power of 0 is 1:

[tex]\[ f(0) = 2 \cdot 1 = 2 \][/tex]

So, for [tex]\( f(x) = 2 \cdot 3^x \)[/tex], the initial value when [tex]\( x = 0 \)[/tex] is 2.

### Evaluating [tex]\( f(x) = 3 \cdot 2^x \)[/tex] at [tex]\( x = 0 \)[/tex]:

[tex]\[ f(0) = 3 \cdot 2^0 \][/tex]
Similarly, any number raised to the power of 0 is 1:

[tex]\[ f(0) = 3 \cdot 1 = 3 \][/tex]

So, for [tex]\( f(x) = 3 \cdot 2^x \)[/tex], the initial value when [tex]\( x = 0 \)[/tex] is 3.

### Conclusion
The exponential function that has an initial value of 2 is [tex]\( f(x) = 2 \cdot 3^x \)[/tex].
Thank you for visiting our platform. We hope you found the answers you were looking for. Come back anytime you need more information. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.