Answer:
B. \(f(x)=5\cdot 3^x\)
Step-by-step explanation:
We have been given 3 function formulas and we are asked to choose the function that grows at the fastest rate for increasing values of x.
Since we know that quadratic function grows faster than a linear function and an exponential function grows faster than a quadratic function, so the function of an exponential function will have the fastest rate for increasing value of x.
Since an exponential function is in form: \(y=a*b^x\).
Upon looking at our given choices we can see that function represented by option A is a linear function and function represented by option C is a quadratic function.
Upon looking at our given choices we can see that function: \(f(x)=5\cdot 3^x\) is an exponential function, therefore, option B is the correct choice.
