Identify the type of function represented by

`f\left(x\right)\ =3\cdot\left(\frac{1}{4}\right)^{x}\ `

1 answer

The function \( f(x) = 3 \cdot \left(\frac{1}{4}\right)^{x} \) represents an exponential function.

In general, an exponential function has the form:

\[ f(x) = a \cdot b^{x} \]

where:

  • \( a \) is a constant (in this case, \( a = 3 \)),
  • \( b \) is the base of the exponential (in this case, \( b = \frac{1}{4} \)),
  • \( x \) is the exponent.

Since \( b = \frac{1}{4} \) is between 0 and 1, this indicates that the function is a decaying exponential function.

In summary, the function \( f(x) = 3 \cdot \left(\frac{1}{4}\right)^{x} \) is an exponential decay function.