To solve for the value of [tex]\( f(t) \)[/tex] in the function [tex]\( f(t) = P e^{rt} \)[/tex], given the constants [tex]\( P = 8 \)[/tex], [tex]\( r = 0.08 \)[/tex], and time [tex]\( t = 8 \)[/tex], we follow these steps:
1. Identify the values provided:
- [tex]\( P = 8 \)[/tex]
- [tex]\( r = 0.08 \)[/tex]
- [tex]\( t = 8 \)[/tex]
2. Substitute these values into the function [tex]\( f(t) = P e^{rt} \)[/tex]:
[tex]\[ f(8) = 8 \cdot e^{0.08 \cdot 8} \][/tex]
3. Calculate the exponent:
[tex]\[ 0.08 \times 8 = 0.64 \][/tex]
4. Raise [tex]\( e \)[/tex] (Euler's number, approximately equal to 2.71828) to the power of 0.64:
[tex]\[ e^{0.64} \approx 1.896 \][/tex]
5. Multiply the result by [tex]\( P \)[/tex]:
[tex]\[ 8 \times 1.896 = 15.168 \][/tex]
6. Round the result to the nearest tenth:
[tex]\[ 15.168 \approx 15.2 \][/tex]
So, the value of [tex]\( f(8) \)[/tex] to the nearest tenth is [tex]\( 15.2 \)[/tex].
Therefore, the correct answer is:
A. 15.2
