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Answer :
To find the approximate value of [tex]\( P \)[/tex] in the function [tex]\( f(t) = P e^{rt} \)[/tex], we use the information that [tex]\( f(4) = 246.4 \)[/tex] when [tex]\( r = 0.04 \)[/tex].
1. Start with the given function:
[tex]\[ f(t) = P e^{rt} \][/tex]
2. Plug in the given values:
We have [tex]\( f(4) = 246.4 \)[/tex], [tex]\( r = 0.04 \)[/tex], and [tex]\( t = 4 \)[/tex]. Substitute these into the function:
[tex]\[ 246.4 = P e^{0.04 \times 4} \][/tex]
3. Simplify the exponent:
[tex]\[ e^{0.04 \times 4} = e^{0.16} \][/tex]
4. Solve for [tex]\( P \)[/tex]:
[tex]\[ P = \frac{246.4}{e^{0.16}} \][/tex]
5. Calculate the approximate value:
After evaluating the expression [tex]\( \frac{246.4}{e^{0.16}} \)[/tex], we find that [tex]\( P \approx 210 \)[/tex].
Thus, the approximate value of [tex]\( P \)[/tex] is closest to option D: 210.
1. Start with the given function:
[tex]\[ f(t) = P e^{rt} \][/tex]
2. Plug in the given values:
We have [tex]\( f(4) = 246.4 \)[/tex], [tex]\( r = 0.04 \)[/tex], and [tex]\( t = 4 \)[/tex]. Substitute these into the function:
[tex]\[ 246.4 = P e^{0.04 \times 4} \][/tex]
3. Simplify the exponent:
[tex]\[ e^{0.04 \times 4} = e^{0.16} \][/tex]
4. Solve for [tex]\( P \)[/tex]:
[tex]\[ P = \frac{246.4}{e^{0.16}} \][/tex]
5. Calculate the approximate value:
After evaluating the expression [tex]\( \frac{246.4}{e^{0.16}} \)[/tex], we find that [tex]\( P \approx 210 \)[/tex].
Thus, the approximate value of [tex]\( P \)[/tex] is closest to option D: 210.
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