Question

Inverse of 20ln(40t − 1200)

Answer 1

The inverse of the function 20ln(40t - 1200) is found through a series of steps that isolate the variable t, resulting in the inverse function t = (e^(y/20) + 1200)/40.

Step-by-step explanation:

The inverse of the function 20ln(40t - 1200) requires us to solve for t in terms of the output variable, normally denoted y. Assuming the function is in the form y = 20ln(40t - 1200), we proceed by isolating the natural logarithm and then the variable t through algebraic manipulation.

1. Divide both sides of the equation by 20: y/20 = ln(40t - 1200).
2. Apply the exponential function e to both sides to cancel the natural logarithm: e^(y/20) = 40t - 1200.
3. Add 1200 to both sides to isolate the term with t: e^(y/20) + 1200 = 40t.
4. Finally, divide both sides by 40 to solve for t: t = (e^(y/20) + 1200)/40.

Thus, the inverse function is t = (e^(y/20) + 1200)/40.