Answer :
To find the value of [tex]\( f\left(\frac{1}{2}\right) \)[/tex] for the exponential function [tex]\( f(x) = 3 \cdot 25^x \)[/tex], we need to substitute [tex]\( x \)[/tex] with [tex]\(\frac{1}{2}\)[/tex] in the function and then simplify.
1. Start with the function:
[tex]\[
f(x) = 3 \cdot 25^x
\][/tex]
2. Substitute [tex]\(x\)[/tex] with [tex]\(\frac{1}{2}\)[/tex]:
[tex]\[
f\left(\frac{1}{2}\right) = 3 \cdot 25^{\frac{1}{2}}
\][/tex]
3. Calculate [tex]\(25^{\frac{1}{2}}\)[/tex]:
- The expression [tex]\(25^{\frac{1}{2}}\)[/tex] is equivalent to the square root of 25.
- The square root of 25 is 5.
4. Now, substitute back the result of the square root:
[tex]\[
f\left(\frac{1}{2}\right) = 3 \cdot 5
\][/tex]
5. Multiply:
[tex]\[
3 \cdot 5 = 15
\][/tex]
So, the value of [tex]\( f\left(\frac{1}{2}\right) \)[/tex] is 15. Thus, the correct answer is 15.
1. Start with the function:
[tex]\[
f(x) = 3 \cdot 25^x
\][/tex]
2. Substitute [tex]\(x\)[/tex] with [tex]\(\frac{1}{2}\)[/tex]:
[tex]\[
f\left(\frac{1}{2}\right) = 3 \cdot 25^{\frac{1}{2}}
\][/tex]
3. Calculate [tex]\(25^{\frac{1}{2}}\)[/tex]:
- The expression [tex]\(25^{\frac{1}{2}}\)[/tex] is equivalent to the square root of 25.
- The square root of 25 is 5.
4. Now, substitute back the result of the square root:
[tex]\[
f\left(\frac{1}{2}\right) = 3 \cdot 5
\][/tex]
5. Multiply:
[tex]\[
3 \cdot 5 = 15
\][/tex]
So, the value of [tex]\( f\left(\frac{1}{2}\right) \)[/tex] is 15. Thus, the correct answer is 15.
