Answer :
To find the approximate value of [tex]\( P \)[/tex], we need to use the information given in the problem. We know that the function is [tex]\( f(t) = P e^{rt} \)[/tex].
We are given:
- [tex]\( f(3) = 191.5 \)[/tex]
- [tex]\( r = 0.03 \)[/tex]
- [tex]\( t = 3 \)[/tex]
Using the function format:
[tex]\[
f(3) = P e^{3r}
\][/tex]
Substituting the given values, we have:
[tex]\[
191.5 = P \times e^{3 \times 0.03}
\][/tex]
First, calculate the exponent:
[tex]\[
e^{3 \times 0.03} = e^{0.09} \approx 1.0941742837052104
\][/tex]
Now substitute this back into the equation:
[tex]\[
191.5 = P \times 1.0941742837052104
\][/tex]
To find [tex]\( P \)[/tex], solve for [tex]\( P \)[/tex]:
[tex]\[
P = \frac{191.5}{1.0941742837052104} \approx 175.01782197944019
\][/tex]
So, the approximate value of [tex]\( P \)[/tex] is [tex]\( 175 \)[/tex]. Therefore, the correct answer is:
A. 175
We are given:
- [tex]\( f(3) = 191.5 \)[/tex]
- [tex]\( r = 0.03 \)[/tex]
- [tex]\( t = 3 \)[/tex]
Using the function format:
[tex]\[
f(3) = P e^{3r}
\][/tex]
Substituting the given values, we have:
[tex]\[
191.5 = P \times e^{3 \times 0.03}
\][/tex]
First, calculate the exponent:
[tex]\[
e^{3 \times 0.03} = e^{0.09} \approx 1.0941742837052104
\][/tex]
Now substitute this back into the equation:
[tex]\[
191.5 = P \times 1.0941742837052104
\][/tex]
To find [tex]\( P \)[/tex], solve for [tex]\( P \)[/tex]:
[tex]\[
P = \frac{191.5}{1.0941742837052104} \approx 175.01782197944019
\][/tex]
So, the approximate value of [tex]\( P \)[/tex] is [tex]\( 175 \)[/tex]. Therefore, the correct answer is:
A. 175
