Question

The temperature inside a certain industrial machine at time t seconds after startup, for 0 < t < 10, is given by h(t) = 4^(2t + 1) - 4^(t + 2) degrees Celsius. How many seconds after startup is the temperature inside the machine equal to 128 degrees Celsius? a) 3/2 b) 2 c) 5/2 d) 3 e) 7/2

Answer 1

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