Answer :
Let's solve the problem step-by-step to find the value of [tex]\( P \)[/tex] in the equation [tex]\( f(t) = P \cdot e^{r \cdot t} \)[/tex].
We are given:
- [tex]\( f(3) = 191.5 \)[/tex]
- [tex]\( r = 0.03 \)[/tex]
The function is:
[tex]\[ f(t) = P \cdot e^{r \cdot t} \][/tex]
In this case:
[tex]\[ f(3) = P \cdot e^{0.03 \times 3} = 191.5 \][/tex]
Now, let's calculate [tex]\( e^{0.03 \times 3} \)[/tex]:
[tex]\[ e^{0.09} \approx 1.0942 \][/tex] (This is a standard exponentiation result; you can use a calculator to verify.)
Now substitute back to solve for [tex]\( P \)[/tex]:
[tex]\[ 191.5 = P \cdot 1.0942 \][/tex]
To find [tex]\( P \)[/tex], divide both sides by 1.0942:
[tex]\[ P = \frac{191.5}{1.0942} \][/tex]
Calculating this gives:
[tex]\[ P \approx 175 \][/tex]
Therefore, the approximate value of [tex]\( P \)[/tex] is 175.
The correct answer is D. 175.
We are given:
- [tex]\( f(3) = 191.5 \)[/tex]
- [tex]\( r = 0.03 \)[/tex]
The function is:
[tex]\[ f(t) = P \cdot e^{r \cdot t} \][/tex]
In this case:
[tex]\[ f(3) = P \cdot e^{0.03 \times 3} = 191.5 \][/tex]
Now, let's calculate [tex]\( e^{0.03 \times 3} \)[/tex]:
[tex]\[ e^{0.09} \approx 1.0942 \][/tex] (This is a standard exponentiation result; you can use a calculator to verify.)
Now substitute back to solve for [tex]\( P \)[/tex]:
[tex]\[ 191.5 = P \cdot 1.0942 \][/tex]
To find [tex]\( P \)[/tex], divide both sides by 1.0942:
[tex]\[ P = \frac{191.5}{1.0942} \][/tex]
Calculating this gives:
[tex]\[ P \approx 175 \][/tex]
Therefore, the approximate value of [tex]\( P \)[/tex] is 175.
The correct answer is D. 175.
