Final answer:
The temperature inside the industrial machine is 128 degrees Celsius 1.5 seconds after startup.
Step-by-step explanation:
To solve this problem, substitute 128 for h(t) in the equation and solve for t:
128 = 4^(2t + 1) - 4^(t + 2)
Solving this equation for t, we find that the solution is t = 3/2 seconds.
In the context of the problem, this means that the temperature inside the industrial machine is 128 degrees Celsius 1.5 seconds after startup.
Learn more about Solving Exponential Equations