Questions: h(t)=t^(3 / 4)-2t^(1 / 4)

Solution Steps

To solve the function \( h(t) = t^{3/4} - 2t^{1/4} \), we can evaluate it for a given value of \( t \). We will write a Python function that takes \( t \) as an input and returns the value of \( h(t) \).

We start by substituting \( t = 4 \) into the function \( h(t) = t^{3/4} - 2t^{1/4} \).

Calculating each term:

• \( t^{3/4} = 4^{3/4} = (2^2)^{3/4} = 2^{3/2} = 2\sqrt{2} \)
• \( t^{1/4} = 4^{1/4} = (2^2)^{1/4} = 2^{1/2} = \sqrt{2} \)

Now substituting these values into the function: \[ h(4) = 2\sqrt{2} - 2(\sqrt{2}) = 2\sqrt{2} - 2\sqrt{2} = 0 \]

The evaluation of \( h(4) \) results in \( 0.0 \).

Final Answer