Question

question 4 of 10
use the function below to find f(1).
f(t) = 2 • \frac{1}{2^{3t}}

a. \frac{1}{8}
b. \frac{1}{4}
c. \frac{1}{2}
d. \frac{1}{3}

Explanation:

Step1: Substitute \( t = 1 \) into \( F(t) \)

Given \( F(t)=2\cdot\frac{1}{2^{3t}} \), substitute \( t = 1 \):
\( F(1)=2\cdot\frac{1}{2^{3\times1}} \)

Step2: Simplify the exponent

Calculate \( 2^{3\times1}=2^3 = 8 \), so:
\( F(1)=2\cdot\frac{1}{8} \)

Step3: Multiply the terms

\( 2\cdot\frac{1}{8}=\frac{2}{8}=\frac{1}{4} \) (Wait, no—wait, let's re - check. Wait, the original function: if it's \( F(t)=2\cdot\frac{1}{2^{3t}} \), when \( t = 1 \), \( 2^{3t}=2^{3}=8 \), so \( \frac{1}{8}\times2=\frac{2}{8}=\frac{1}{4} \)? Wait, but let's check the options. Option B is \( \frac{1}{4} \). Wait, but maybe I misread the function. Wait, the function is written as \( F(t)=2\bullet\frac{1}{2^{3t}} \). So when \( t = 1 \), \( 3t = 3 \), \( 2^{3}=8 \), so \( \frac{1}{8}\times2=\frac{2}{8}=\frac{1}{4} \). So the value of \( F(1) \) is \( \frac{1}{4} \).

Answer:

B. \(\frac{1}{4}\)