Answer :
To solve this problem, we need to evaluate the function [tex]\( f(x) = 3 \cdot 25^x \)[/tex] at [tex]\( x = \frac{1}{2} \)[/tex].
Here's how you can approach it step-by-step:
1. Understand the function:
The function [tex]\( f(x) = 3 \cdot 25^x \)[/tex] is an exponential function where the base of the exponent is 25 and the coefficient is 3.
2. Substitute [tex]\( x = \frac{1}{2} \)[/tex] into the function:
We need to find [tex]\( f\left(\frac{1}{2}\right) \)[/tex], which is calculated by substituting [tex]\(\frac{1}{2}\)[/tex] in place of [tex]\( x \)[/tex].
3. Calculate [tex]\( 25^{1/2} \)[/tex]:
[tex]\( 25^{1/2} \)[/tex] represents the square root of 25. The square root of 25 is 5, so [tex]\( 25^{1/2} = 5 \)[/tex].
4. Calculate [tex]\( f\left(\frac{1}{2}\right) \)[/tex]:
Replace [tex]\( 25^{1/2} \)[/tex] with 5 in the function:
[tex]\( f\left(\frac{1}{2}\right) = 3 \cdot 25^{1/2} = 3 \cdot 5 \)[/tex].
5. Multiply to find the final answer:
Now, multiply 3 by 5:
[tex]\( f\left(\frac{1}{2}\right) = 3 \times 5 = 15 \)[/tex].
Therefore, the value of [tex]\( f\left(\frac{1}{2}\right) \)[/tex] is 15.
Here's how you can approach it step-by-step:
1. Understand the function:
The function [tex]\( f(x) = 3 \cdot 25^x \)[/tex] is an exponential function where the base of the exponent is 25 and the coefficient is 3.
2. Substitute [tex]\( x = \frac{1}{2} \)[/tex] into the function:
We need to find [tex]\( f\left(\frac{1}{2}\right) \)[/tex], which is calculated by substituting [tex]\(\frac{1}{2}\)[/tex] in place of [tex]\( x \)[/tex].
3. Calculate [tex]\( 25^{1/2} \)[/tex]:
[tex]\( 25^{1/2} \)[/tex] represents the square root of 25. The square root of 25 is 5, so [tex]\( 25^{1/2} = 5 \)[/tex].
4. Calculate [tex]\( f\left(\frac{1}{2}\right) \)[/tex]:
Replace [tex]\( 25^{1/2} \)[/tex] with 5 in the function:
[tex]\( f\left(\frac{1}{2}\right) = 3 \cdot 25^{1/2} = 3 \cdot 5 \)[/tex].
5. Multiply to find the final answer:
Now, multiply 3 by 5:
[tex]\( f\left(\frac{1}{2}\right) = 3 \times 5 = 15 \)[/tex].
Therefore, the value of [tex]\( f\left(\frac{1}{2}\right) \)[/tex] is 15.
