Answer :

We start with the equation

[tex]$$
1.82 \, e^t = 38.8.
$$[/tex]

Step 1. Isolate the exponential term

Divide both sides of the equation by 1.82:

[tex]$$
e^t = \frac{38.8}{1.82} \approx 21.31868.
$$[/tex]

Step 2. Take the natural logarithm

Since the natural logarithm is the inverse of the exponential function, take [tex]$\ln$[/tex] on both sides:

[tex]$$
t = \ln\left(21.31868\right).
$$[/tex]

Calculating the natural logarithm gives approximately:

[tex]$$
t \approx 3.05958.
$$[/tex]

Thus, the solution to the equation is

[tex]$$
t \approx 3.06.
$$[/tex]

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