Final answer:
To find the input x that would give the function f(x) = 5x2^x an output of 200, we need to solve the equation 5x*2^x = 200. Algebraic solutions are complex due to the x in the base and exponent, thus numerical methods or graphing would typically be used to approximate a solution.
Step-by-step explanation:
It is possible to determine if the function f(x) = 5x2^x can output the value 200 and what input x would produce that output. To find the value of x that makes f(x) = 200, we can set up the equation 5x*2^x = 200 and solve for x.
However, this equation is not straightforward to solve algebraically due to the x being in both the base and the exponent. Numerical methods or graphing tools would typically be employed to find an approximate solution.
If such tools indicate that there is an x within the given range that satisfies the equation, then the function can have an output of 200. If no solution exists within the range, then the function cannot output the value 200 between 0 and 20.