Answer :
To solve the equation [tex]\(2.75 \cdot e^t = 38.6\)[/tex] for [tex]\(t\)[/tex], follow these steps:
1. Isolate [tex]\(e^t\)[/tex]:
Begin by dividing both sides of the equation by 2.75 to isolate the term with [tex]\(e^t\)[/tex].
[tex]\[
e^t = \frac{38.6}{2.75}
\][/tex]
2. Calculate the value of [tex]\(\frac{38.6}{2.75}\)[/tex]:
[tex]\[
e^t = 14.0364
\][/tex]
3. Solve for [tex]\(t\)[/tex] using the natural logarithm:
Since [tex]\(e^t = 14.0364\)[/tex], take the natural logarithm (ln) of both sides to find [tex]\(t\)[/tex].
[tex]\[
t = \ln(14.0364)
\][/tex]
4. Find the value of [tex]\(t\)[/tex]:
Calculate the natural logarithm to find the approximate value of [tex]\(t\)[/tex].
[tex]\[
t \approx 2.6417
\][/tex]
So, the solution to the equation [tex]\(2.75 \cdot e^t = 38.6\)[/tex] is approximately [tex]\(t \approx 2.6417\)[/tex].
1. Isolate [tex]\(e^t\)[/tex]:
Begin by dividing both sides of the equation by 2.75 to isolate the term with [tex]\(e^t\)[/tex].
[tex]\[
e^t = \frac{38.6}{2.75}
\][/tex]
2. Calculate the value of [tex]\(\frac{38.6}{2.75}\)[/tex]:
[tex]\[
e^t = 14.0364
\][/tex]
3. Solve for [tex]\(t\)[/tex] using the natural logarithm:
Since [tex]\(e^t = 14.0364\)[/tex], take the natural logarithm (ln) of both sides to find [tex]\(t\)[/tex].
[tex]\[
t = \ln(14.0364)
\][/tex]
4. Find the value of [tex]\(t\)[/tex]:
Calculate the natural logarithm to find the approximate value of [tex]\(t\)[/tex].
[tex]\[
t \approx 2.6417
\][/tex]
So, the solution to the equation [tex]\(2.75 \cdot e^t = 38.6\)[/tex] is approximately [tex]\(t \approx 2.6417\)[/tex].
