Answer :
To solve for [tex]\( P \)[/tex], we know from the problem that:
[tex]\[ f(t) = P \cdot e^{r \cdot t} \][/tex]
We're given:
- [tex]\( f(4) = 246.4 \)[/tex]
- [tex]\( r = 0.04 \)[/tex]
- [tex]\( t = 4 \)[/tex]
We need to find [tex]\( P \)[/tex].
1. Substitute the values into the function:
[tex]\[ 246.4 = P \cdot e^{0.04 \cdot 4} \][/tex]
2. Simplify the exponent:
[tex]\[ e^{0.04 \cdot 4} = e^{0.16} \][/tex]
3. Calculate [tex]\( e^{0.16} \)[/tex].
4. Solve for [tex]\( P \)[/tex] by dividing both sides of the equation by [tex]\( e^{0.16} \)[/tex]:
[tex]\[ P = \frac{246.4}{e^{0.16}} \][/tex]
Using the above steps, the approximate value of [tex]\( P \)[/tex] is found to be about 210.
Therefore, the correct answer is B. 210.
[tex]\[ f(t) = P \cdot e^{r \cdot t} \][/tex]
We're given:
- [tex]\( f(4) = 246.4 \)[/tex]
- [tex]\( r = 0.04 \)[/tex]
- [tex]\( t = 4 \)[/tex]
We need to find [tex]\( P \)[/tex].
1. Substitute the values into the function:
[tex]\[ 246.4 = P \cdot e^{0.04 \cdot 4} \][/tex]
2. Simplify the exponent:
[tex]\[ e^{0.04 \cdot 4} = e^{0.16} \][/tex]
3. Calculate [tex]\( e^{0.16} \)[/tex].
4. Solve for [tex]\( P \)[/tex] by dividing both sides of the equation by [tex]\( e^{0.16} \)[/tex]:
[tex]\[ P = \frac{246.4}{e^{0.16}} \][/tex]
Using the above steps, the approximate value of [tex]\( P \)[/tex] is found to be about 210.
Therefore, the correct answer is B. 210.
