Answer :
Let's solve the problem step-by-step to find the approximate value of [tex]\( P \)[/tex].
We are given the function [tex]\( f(t) = P e^{rt} \)[/tex] and specific values for [tex]\( f(5) \)[/tex], [tex]\( r \)[/tex], and [tex]\( t \)[/tex]:
1. [tex]\( f(5) = 288.9 \)[/tex]
2. [tex]\( r = 0.05 \)[/tex]
3. [tex]\( t = 5 \)[/tex]
We need to find the value of [tex]\( P \)[/tex]. Here's the step-by-step solution:
1. Plug the given values into the function:
[tex]\[
f(5) = P e^{0.05 \times 5}
\][/tex]
2. Simplify the exponent:
[tex]\[
0.05 \times 5 = 0.25
\][/tex]
3. Substitute this back into the function:
[tex]\[
288.9 = P e^{0.25}
\][/tex]
4. Calculate [tex]\( e^{0.25} \)[/tex]:
[tex]\[
e^{0.25} \approx 1.284
\][/tex]
5. Now, we can rewrite the equation:
[tex]\[
288.9 = P \times 1.284
\][/tex]
6. To find [tex]\( P \)[/tex], divide both sides of the equation by 1.284:
[tex]\[
P = \frac{288.9}{1.284} \approx 225
\][/tex]
Therefore, the approximate value of [tex]\( P \)[/tex] is 225.
So, the correct answer is:
C. 225
We are given the function [tex]\( f(t) = P e^{rt} \)[/tex] and specific values for [tex]\( f(5) \)[/tex], [tex]\( r \)[/tex], and [tex]\( t \)[/tex]:
1. [tex]\( f(5) = 288.9 \)[/tex]
2. [tex]\( r = 0.05 \)[/tex]
3. [tex]\( t = 5 \)[/tex]
We need to find the value of [tex]\( P \)[/tex]. Here's the step-by-step solution:
1. Plug the given values into the function:
[tex]\[
f(5) = P e^{0.05 \times 5}
\][/tex]
2. Simplify the exponent:
[tex]\[
0.05 \times 5 = 0.25
\][/tex]
3. Substitute this back into the function:
[tex]\[
288.9 = P e^{0.25}
\][/tex]
4. Calculate [tex]\( e^{0.25} \)[/tex]:
[tex]\[
e^{0.25} \approx 1.284
\][/tex]
5. Now, we can rewrite the equation:
[tex]\[
288.9 = P \times 1.284
\][/tex]
6. To find [tex]\( P \)[/tex], divide both sides of the equation by 1.284:
[tex]\[
P = \frac{288.9}{1.284} \approx 225
\][/tex]
Therefore, the approximate value of [tex]\( P \)[/tex] is 225.
So, the correct answer is:
C. 225
