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Answer :
We are given the function
[tex]$$
f(t) = P e^{rt},
$$[/tex]
with the function value at [tex]$t=4$[/tex] provided as
[tex]$$
f(4) = 246.4,
$$[/tex]
and the rate [tex]$r = 0.04$[/tex]. Substituting [tex]$t = 4$[/tex] into the function, we have
[tex]$$
246.4 = P e^{0.04 \cdot 4}.
$$[/tex]
Notice that [tex]$0.04 \cdot 4 = 0.16$[/tex], so the equation becomes
[tex]$$
246.4 = P e^{0.16}.
$$[/tex]
To solve for [tex]$P$[/tex], divide both sides by [tex]$e^{0.16}$[/tex]:
[tex]$$
P = \frac{246.4}{e^{0.16}}.
$$[/tex]
Evaluating [tex]$e^{0.16}$[/tex] gives approximately 1.17351. Therefore,
[tex]$$
P \approx \frac{246.4}{1.17351} \approx 210.
$$[/tex]
Thus, the approximate value of [tex]$P$[/tex] is [tex]$\boxed{210}$[/tex].
[tex]$$
f(t) = P e^{rt},
$$[/tex]
with the function value at [tex]$t=4$[/tex] provided as
[tex]$$
f(4) = 246.4,
$$[/tex]
and the rate [tex]$r = 0.04$[/tex]. Substituting [tex]$t = 4$[/tex] into the function, we have
[tex]$$
246.4 = P e^{0.04 \cdot 4}.
$$[/tex]
Notice that [tex]$0.04 \cdot 4 = 0.16$[/tex], so the equation becomes
[tex]$$
246.4 = P e^{0.16}.
$$[/tex]
To solve for [tex]$P$[/tex], divide both sides by [tex]$e^{0.16}$[/tex]:
[tex]$$
P = \frac{246.4}{e^{0.16}}.
$$[/tex]
Evaluating [tex]$e^{0.16}$[/tex] gives approximately 1.17351. Therefore,
[tex]$$
P \approx \frac{246.4}{1.17351} \approx 210.
$$[/tex]
Thus, the approximate value of [tex]$P$[/tex] is [tex]$\boxed{210}$[/tex].
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