Question

The value 2 · 2 · 2 · 2 · 2 · 4.7 is the output value of an exponential function of the form f x = a · b x , where a and b are constants. which of the following describes the function and input value that corresponds to this output value?

Answer 1

The given expression can be written as an exponential function, f(x) = 4.7 · 2x, with an input value of x = 5.

Step-by-step explanation:

The given expression 2 · 2 · 2 · 2 · 2 · 4.7 can be written as 25 · 4.7.

This can be expressed in the form of an exponential function, f(x) = a · bx, where a = 4.7 and b = 2.

So, the function and input value that corresponds to this output value is f(x) = 4.7 · 2x, and the input value is x = 5.

Answer 2

The output value of 150.4 corresponds to the exponential function f(x) = 4.7 · 2^x with an input value of x = 5.

Step-by-step explanation:

The question inquires about the properties of an exponential function that would produce the output given by the expression 2 · 2 · 2 · 2 · 2 · 4.7. To frame the expression in terms of an exponential function of the form f(x) = a · bx, we need to identify the constants a and b and the input value x.

Firstly, let's simplify the expression given: 2 · 2 · 2 · 2 · 2 · 4.7 equals 25 · 4.7. Recall from exponential arithmetic that increasing by a factor of 2n, where 2 is the base and n is the number of times, produces 25 = 32. Multiplying by 4.7, we get 32 · 4.7 = 150.4.

With regards to the exponential function f(x), the output 150.4 must equal a · bx. If we consider a to be 4.7 (the non-exponential part of the original expression) and b to be 2 (the base of the exponent), then the exponent x is 5 because 25 represents the exponential part of the original expression.

Therefore, the function and input value that corresponds to this output value is f(x) = 4.7 · 2x with x = 5, as this configuration reproduces the value of 150.4 when calculated.