Let's solve for the value of the function [tex]\( f(t) = P e^{rt} \)[/tex], given the values [tex]\( P = 3 \)[/tex], [tex]\( r = 0.03 \)[/tex], and we need to find [tex]\( f(3) \)[/tex].
First, substitute the given values into the function:
[tex]\[ f(3) = 3 e^{0.03 \times 3} \][/tex]
Now, simplify the exponent:
[tex]\[ 0.03 \times 3 = 0.09 \][/tex]
Thus, the expression now becomes:
[tex]\[ f(3) = 3 e^{0.09} \][/tex]
To find the value of [tex]\( f(3) \)[/tex], we need the value of the mathematical constant [tex]\( e \)[/tex] raised to the power of [tex]\( 0.09 \)[/tex]. Using the fact that [tex]\( e^{0.09} \)[/tex] can be computed (typically with a calculator or numerical methods), we get the following value:
[tex]\[ e^{0.09} \approx 1.09417 \][/tex]
Next, multiply this result by [tex]\( P \)[/tex]:
[tex]\[ 3 \times 1.09417 \approx 3.28251 \][/tex]
Rounding this value to the nearest tenth:
[tex]\[ 3.28251 \approx 3.3 \][/tex]
Therefore, the value of [tex]\( f(3) \)[/tex] rounded to the nearest tenth is [tex]\( 3.3 \)[/tex].
So, the correct answer is:
D. 3.3
