Final answer:
The value of the exponential function f(1)= 5*1*4^1 for f(x) = 5x4^x is 20. The given options in the student's question do not include this answer, indicating an error in the question. The correct understanding of exponents is crucial in solving such problems.
"The correct option is approximately option C"
Step-by-step explanation:
The exponential function in question is f(x)= 5x4^x. To find the value of f(1), we substitute x with 1, which gives us f(1) = 5*1*4^1.
Since any number to the power of 1 is the number itself, we have 5*1*4^1 = 5*1*4 = 20. However, there appears to be an error in the student's question as the options provided (80, 10, 5, 40) do not include the correct answer, which is 20. Therefore, none of the given choices are correct.
It is also important to understand the rules that govern exponents to address similar errors. When a base is raised to an exponent, the base is multiplied by itself as many times as the value of the exponent indicates. For example, 4^3 is shorthand for 4 * 4 * 4, which equals 64.
Understanding the fundamental properties of exponents can also shed light on more complex operations involving exponents, such as multiplying powers with the same base or raising a power to another power.