Answer :

We start with the equation

[tex]$$
2.17 e^t = 35.8.
$$[/tex]

Step 1. Isolate [tex]$e^t$[/tex]:

Divide both sides by [tex]$2.17$[/tex]:

[tex]$$
e^t = \frac{35.8}{2.17} \approx 16.4977.
$$[/tex]

Step 2. Take the natural logarithm:

To solve for [tex]$t$[/tex], take the natural logarithm of both sides:

[tex]$$
\ln(e^t) = \ln(16.4977).
$$[/tex]

Since [tex]$\ln(e^t) = t$[/tex], this simplifies to:

[tex]$$
t = \ln(16.4977).
$$[/tex]

Step 3. Calculate [tex]$t$[/tex]:

Computing the natural logarithm,

[tex]$$
t \approx 2.8032.
$$[/tex]

Thus, the solution rounded to four decimal places is

[tex]$$
\boxed{2.8032}.
$$[/tex]

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Rewritten by : Barada