Questions: Solve for t e^(-0.54 t)=0.37 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution is t= (Type an integer or a decimal. Do not round until the final answer. Then round to four decimal places as needed. Use a comma to separate answers as needed.) B. The solution is not a real number.

Solve for t
e^(-0.54 t)=0.37

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The solution is t=
(Type an integer or a decimal. Do not round until the final answer. Then round to four decimal places as needed. Use a comma to separate answers as needed.)
B. The solution is not a real number.

Transcript text: Solve for $t$ \[ e^{-0.54 t}=0.37 \] Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution is $t=$ $\square$ (Type an integer or a decimal. Do not round until the final answer. Then round to four decimal places as needed. Use a comma to separate answers as needed.) B. The solution is not a real number.

Solution

Solution Steps

Step 1: Start with the equation

Given the equation $e^{-k t} = P$, where $e$ is the base of the natural logarithm, $t$ is the variable to solve for, $k$ is a constant coefficient of $t$, and $P$ is a constant representing the value of the exponential expression.

Step 2: Take the natural logarithm (ln) of both sides

Taking the natural logarithm of both sides of the equation to get rid of the exponential, we get $-k t = \ln(P)$.

Step 3: Solve for $t$

Solving for $t$ by dividing both sides by $-k$, we find $t = -\frac{\ln(P)}{k}$. Substituting the given values, we get $t = 1.841$.