Question
What is the domain of the exponential function shown below? \( \begin{array}{l}F(x)=2 \cdot\left(\frac{1}{10}\right)^{x} \\ \text { A. } x>0 \\ \text { B. } x<0 \\ \text { C. All real numbers } \\ \text { D. All real numbers except } 2\end{array} \) ?
Ask by Davison Bartlett. in the United States
Dec 15,2024
Real Tutor Solution
Tutor-Verified Answer
Answer
The domain is all real numbers.
Solution
The exponential function given is \( F(x) = 2 \cdot \left(\frac{1}{10}\right)^{x} \).
The domain of an exponential function is typically all real numbers, as you can input any real number \( x \) into the function and it will produce a valid output.
In this case, there are no restrictions on \( x \) that would limit the domain. Therefore, the correct answer is:
**C. All real numbers**.
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Simplify this solution The Deep Dive
The domain of the function \(F(x) = 2 \cdot \left(\frac{1}{10}\right)^{x}\) is actually all real numbers. You can input any real number for \(x\), and the function will produce a valid output because exponential functions are defined for all values of \(x\). So, the correct answer would be C. All real numbers! Exponential functions are used in various fields such as finance for calculating compound interest or in biology for modeling population growth. Understanding the domain helps in applying these concepts effectively, ensuring accurate predictions and analyses in real-world scenarios. So, dive into the fascinating world of exponential growth and decay!
