Answer :
Certainly! Let's solve the equation step by step.
We are given the equation:
[tex]\[ 2.75 \times e^t = 38.6 \][/tex]
Our goal is to solve for [tex]\( t \)[/tex].
### Step 1: Isolate [tex]\( e^t \)[/tex]
First, divide both sides of the equation by 2.75 to isolate [tex]\( e^t \)[/tex]:
[tex]\[ e^t = \frac{38.6}{2.75} \][/tex]
### Step 2: Calculate the value
Next, calculate the division on the right side:
[tex]\[ e^t = 14.036363636363637 \][/tex]
### Step 3: Solve for [tex]\( t \)[/tex]
To solve for [tex]\( t \)[/tex], we need to take the natural logarithm (ln) of both sides because the natural logarithm is the inverse of the exponential function.
[tex]\[ t = \ln(14.036363636363637) \][/tex]
### Step 4: Compute the natural logarithm
Now, calculate the natural logarithm:
[tex]\[ t \approx 2.6416513647923052 \][/tex]
So, the solution to the equation is approximately [tex]\( t = 2.6417 \)[/tex] (rounded to four decimal places). This is the value of [tex]\( t \)[/tex] that satisfies the original equation.
We are given the equation:
[tex]\[ 2.75 \times e^t = 38.6 \][/tex]
Our goal is to solve for [tex]\( t \)[/tex].
### Step 1: Isolate [tex]\( e^t \)[/tex]
First, divide both sides of the equation by 2.75 to isolate [tex]\( e^t \)[/tex]:
[tex]\[ e^t = \frac{38.6}{2.75} \][/tex]
### Step 2: Calculate the value
Next, calculate the division on the right side:
[tex]\[ e^t = 14.036363636363637 \][/tex]
### Step 3: Solve for [tex]\( t \)[/tex]
To solve for [tex]\( t \)[/tex], we need to take the natural logarithm (ln) of both sides because the natural logarithm is the inverse of the exponential function.
[tex]\[ t = \ln(14.036363636363637) \][/tex]
### Step 4: Compute the natural logarithm
Now, calculate the natural logarithm:
[tex]\[ t \approx 2.6416513647923052 \][/tex]
So, the solution to the equation is approximately [tex]\( t = 2.6417 \)[/tex] (rounded to four decimal places). This is the value of [tex]\( t \)[/tex] that satisfies the original equation.
