Question
Identify the type of function represented by
`f\left(x\right)\ =3\cdot\left(\frac{1}{4}\right)^{x}\ `
`f\left(x\right)\ =3\cdot\left(\frac{1}{4}\right)^{x}\ `
Answers
GPT-4o mini
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.
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.