Answer :
To solve the problem, we have the function [tex]\( f(t) = P \cdot e^{r \cdot t} \)[/tex], where we know the following:
- [tex]\( f(3) = 191.5 \)[/tex]
- [tex]\( r = 0.03 \)[/tex]
- [tex]\( t = 3 \)[/tex]
Our goal is to find the value of [tex]\( P \)[/tex].
1. Substitute the known values into the function:
[tex]\[
f(3) = P \cdot e^{0.03 \cdot 3}
\][/tex]
2. Replace [tex]\( f(3) \)[/tex] with 191.5:
[tex]\[
191.5 = P \cdot e^{0.09}
\][/tex]
3. Calculate [tex]\( e^{0.09} \)[/tex] approximately. We know that [tex]\( e^{0.09} \approx 1.09417 \)[/tex].
4. Rearrange the equation to solve for [tex]\( P \)[/tex]:
[tex]\[
P = \frac{191.5}{1.09417}
\][/tex]
5. Calculate the value of [tex]\( P \)[/tex]:
[tex]\[
P \approx 175.018
\][/tex]
The closest answer to this calculation is option B, 175. Therefore, the approximate value of [tex]\( P \)[/tex] is 175.
- [tex]\( f(3) = 191.5 \)[/tex]
- [tex]\( r = 0.03 \)[/tex]
- [tex]\( t = 3 \)[/tex]
Our goal is to find the value of [tex]\( P \)[/tex].
1. Substitute the known values into the function:
[tex]\[
f(3) = P \cdot e^{0.03 \cdot 3}
\][/tex]
2. Replace [tex]\( f(3) \)[/tex] with 191.5:
[tex]\[
191.5 = P \cdot e^{0.09}
\][/tex]
3. Calculate [tex]\( e^{0.09} \)[/tex] approximately. We know that [tex]\( e^{0.09} \approx 1.09417 \)[/tex].
4. Rearrange the equation to solve for [tex]\( P \)[/tex]:
[tex]\[
P = \frac{191.5}{1.09417}
\][/tex]
5. Calculate the value of [tex]\( P \)[/tex]:
[tex]\[
P \approx 175.018
\][/tex]
The closest answer to this calculation is option B, 175. Therefore, the approximate value of [tex]\( P \)[/tex] is 175.
