Answer :
We are given the function
[tex]$$
f(t)=P e^{rt},
$$[/tex]
with [tex]$r=0.04$[/tex] and [tex]$t=4$[/tex]. This means
[tex]$$
f(4)=P e^{0.04\times4}=P e^{0.16}.
$$[/tex]
Since [tex]$f(4)=246.4$[/tex], we have:
[tex]$$
246.4=P e^{0.16}.
$$[/tex]
To solve for [tex]$P$[/tex], divide both sides of the equation by [tex]$e^{0.16}$[/tex]:
[tex]$$
P=\frac{246.4}{e^{0.16}}.
$$[/tex]
Evaluating the value, we have that [tex]$e^{0.16}\approx1.17351$[/tex]. Therefore,
[tex]$$
P\approx\frac{246.4}{1.17351}\approx209.97.
$$[/tex]
This value is approximately [tex]$210$[/tex], which corresponds to option B.
Thus, the approximate value of [tex]$P$[/tex] is [tex]$\boxed{210}$[/tex].
[tex]$$
f(t)=P e^{rt},
$$[/tex]
with [tex]$r=0.04$[/tex] and [tex]$t=4$[/tex]. This means
[tex]$$
f(4)=P e^{0.04\times4}=P e^{0.16}.
$$[/tex]
Since [tex]$f(4)=246.4$[/tex], we have:
[tex]$$
246.4=P e^{0.16}.
$$[/tex]
To solve for [tex]$P$[/tex], divide both sides of the equation by [tex]$e^{0.16}$[/tex]:
[tex]$$
P=\frac{246.4}{e^{0.16}}.
$$[/tex]
Evaluating the value, we have that [tex]$e^{0.16}\approx1.17351$[/tex]. Therefore,
[tex]$$
P\approx\frac{246.4}{1.17351}\approx209.97.
$$[/tex]
This value is approximately [tex]$210$[/tex], which corresponds to option B.
Thus, the approximate value of [tex]$P$[/tex] is [tex]$\boxed{210}$[/tex].
