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Answer :
Let's solve the problem step-by-step.
We are given that the function is [tex]\( f(t) = P e^t \)[/tex] and that [tex]\( f(4) = 246.4 \)[/tex] when [tex]\( r = 0.04 \)[/tex]. Here's how we approach it:
1. Identify the Variables:
- [tex]\( f(4) = 246.4 \)[/tex]
- [tex]\( r = 0.04 \)[/tex], which is actually referring to the interest rate or growth rate but in this case, we consider the given function [tex]\( f(t) = P e^t \)[/tex].
2. Correct Interpretation:
- The original statement [tex]\( f(4) \)[/tex] relates to when [tex]\( t = 4 \)[/tex], not when [tex]\( r = 0.04 \)[/tex]. So, our equation becomes:
[tex]\[
f(4) = P e^4 = 246.4
\][/tex]
3. Solve for [tex]\( P \)[/tex]:
- We have the equation:
[tex]\[
P e^4 = 246.4
\][/tex]
- To solve for [tex]\( P \)[/tex], divide both sides by [tex]\( e^4 \)[/tex]:
[tex]\[
P = \frac{246.4}{e^4}
\][/tex]
4. Calculate [tex]\( P \)[/tex]:
- First, find [tex]\( e^4 \approx 54.598 \)[/tex].
- Now compute:
[tex]\[
P = \frac{246.4}{54.598} \approx 4.51
\][/tex]
5. Compare with Choices:
- None of the choices provided (210, 289, 50, 1220) are close to 4.51, which indicates there's a misunderstanding with the context or potentially a mistake in the problem setup if interpreted straightforwardly.
In practical executions or problems, always cross-reference the context or values. However, based on given choices and calculations, none of the provided options match the likely realistic computation scenario unless there is additional context or a typographical issue in the problem which should be checked with the problem source.
We are given that the function is [tex]\( f(t) = P e^t \)[/tex] and that [tex]\( f(4) = 246.4 \)[/tex] when [tex]\( r = 0.04 \)[/tex]. Here's how we approach it:
1. Identify the Variables:
- [tex]\( f(4) = 246.4 \)[/tex]
- [tex]\( r = 0.04 \)[/tex], which is actually referring to the interest rate or growth rate but in this case, we consider the given function [tex]\( f(t) = P e^t \)[/tex].
2. Correct Interpretation:
- The original statement [tex]\( f(4) \)[/tex] relates to when [tex]\( t = 4 \)[/tex], not when [tex]\( r = 0.04 \)[/tex]. So, our equation becomes:
[tex]\[
f(4) = P e^4 = 246.4
\][/tex]
3. Solve for [tex]\( P \)[/tex]:
- We have the equation:
[tex]\[
P e^4 = 246.4
\][/tex]
- To solve for [tex]\( P \)[/tex], divide both sides by [tex]\( e^4 \)[/tex]:
[tex]\[
P = \frac{246.4}{e^4}
\][/tex]
4. Calculate [tex]\( P \)[/tex]:
- First, find [tex]\( e^4 \approx 54.598 \)[/tex].
- Now compute:
[tex]\[
P = \frac{246.4}{54.598} \approx 4.51
\][/tex]
5. Compare with Choices:
- None of the choices provided (210, 289, 50, 1220) are close to 4.51, which indicates there's a misunderstanding with the context or potentially a mistake in the problem setup if interpreted straightforwardly.
In practical executions or problems, always cross-reference the context or values. However, based on given choices and calculations, none of the provided options match the likely realistic computation scenario unless there is additional context or a typographical issue in the problem which should be checked with the problem source.
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