To find the value of [tex]\( f(t) \)[/tex] where [tex]\( f(t) = P e^{rt} \)[/tex], given that [tex]\( P = 3 \)[/tex], [tex]\( r = 0.03 \)[/tex], and [tex]\( t = 3 \)[/tex], let's break down the process step by step.
1. Plug in the values:
- [tex]\( P = 3 \)[/tex]
- [tex]\( r = 0.03 \)[/tex]
- [tex]\( t = 3 \)[/tex]
2. Set up the function with these values:
[tex]\[
f(3) = 3 \cdot e^{0.03 \cdot 3}
\][/tex]
3. Simplify the exponent:
[tex]\[
r \times t = 0.03 \times 3 = 0.09
\][/tex]
Therefore, the function becomes:
[tex]\[
f(3) = 3 \cdot e^{0.09}
\][/tex]
4. Evaluate the exponential part [tex]\( e^{0.09} \)[/tex]:
[tex]\[
e^{0.09} \approx 1.094174
\][/tex]
5. Multiply by [tex]\( P = 3 \)[/tex]:
[tex]\[
f(3) = 3 \cdot 1.094174 \approx 3.282522
\][/tex]
6. Round the result to the nearest tenth:
[tex]\[
3.282522 \approx 3.3
\][/tex]
Thus, the value of [tex]\( f(3) \)[/tex] to the nearest tenth is:
[tex]\[
\boxed{3.3}
\][/tex]
So the correct answer is:
C. 3.3
