Answer :
We are given the function
[tex]$$
f(t) = P e^{rt}
$$[/tex]
and the information that
[tex]$$
f(4) = 246.4 \quad \text{with} \quad r = 0.04.
$$[/tex]
This means that
[tex]$$
P e^{0.04 \times 4} = 246.4.
$$[/tex]
1. First, compute the exponent:
[tex]$$
0.04 \times 4 = 0.16.
$$[/tex]
2. Substitute the exponent back into the equation:
[tex]$$
P e^{0.16} = 246.4.
$$[/tex]
3. Solve for [tex]$P$[/tex] by dividing both sides by [tex]$e^{0.16}$[/tex]:
[tex]$$
P = \frac{246.4}{e^{0.16}}.
$$[/tex]
4. Evaluating [tex]$e^{0.16}$[/tex] gives approximately:
[tex]$$
e^{0.16} \approx 1.17351.
$$[/tex]
5. Now, substitute this value into the equation:
[tex]$$
P \approx \frac{246.4}{1.17351} \approx 209.97.
$$[/tex]
This value is nearly [tex]$210$[/tex], so the approximate value of [tex]$P$[/tex] is [tex]$210$[/tex]. Therefore, the correct answer is option B.
[tex]$$
f(t) = P e^{rt}
$$[/tex]
and the information that
[tex]$$
f(4) = 246.4 \quad \text{with} \quad r = 0.04.
$$[/tex]
This means that
[tex]$$
P e^{0.04 \times 4} = 246.4.
$$[/tex]
1. First, compute the exponent:
[tex]$$
0.04 \times 4 = 0.16.
$$[/tex]
2. Substitute the exponent back into the equation:
[tex]$$
P e^{0.16} = 246.4.
$$[/tex]
3. Solve for [tex]$P$[/tex] by dividing both sides by [tex]$e^{0.16}$[/tex]:
[tex]$$
P = \frac{246.4}{e^{0.16}}.
$$[/tex]
4. Evaluating [tex]$e^{0.16}$[/tex] gives approximately:
[tex]$$
e^{0.16} \approx 1.17351.
$$[/tex]
5. Now, substitute this value into the equation:
[tex]$$
P \approx \frac{246.4}{1.17351} \approx 209.97.
$$[/tex]
This value is nearly [tex]$210$[/tex], so the approximate value of [tex]$P$[/tex] is [tex]$210$[/tex]. Therefore, the correct answer is option B.
