High School

Dear beloved readers, welcome to our website! We hope your visit here brings you valuable insights and meaningful inspiration. Thank you for taking the time to stop by and explore the content we've prepared for you.
------------------------------------------------ If [tex]f(5)=288.9[/tex] when [tex]r=0.05[/tex] for the function [tex]f(t)=P e^{rt}[/tex], then what is the approximate value of [tex]P[/tex]?

A. 371
B. 3520
C. 225
D. 24

Answer :

To find the approximate value of [tex]\( P \)[/tex], we need to use the function [tex]\( f(t) = P \cdot e^{r \cdot t} \)[/tex]. We are given that [tex]\( f(5) = 288.9 \)[/tex] and [tex]\( r = 0.05 \)[/tex].

Here’s how we can find [tex]\( P \)[/tex]:

1. Set up the equation for [tex]\( f(t) \)[/tex]:
[tex]\[
288.9 = P \cdot e^{0.05 \cdot 5}
\][/tex]

2. Calculate the exponent:
[tex]\[
e^{0.05 \cdot 5} = e^{0.25}
\][/tex]

3. Calculate the approximate value of [tex]\( e^{0.25} \)[/tex]:
[tex]\[
e^{0.25} \approx 1.28
\][/tex]
(Note: This is an approximation based on typical values.)

4. Solve for [tex]\( P \)[/tex]:
[tex]\[
P = \frac{288.9}{e^{0.25}}
\][/tex]

5. Substitute the value of [tex]\( e^{0.25} \)[/tex] into the equation:
[tex]\[
P = \frac{288.9}{1.28}
\][/tex]

6. Calculate [tex]\( P \)[/tex]:
[tex]\[
P \approx 225
\][/tex]

Therefore, the approximate value of [tex]\( P \)[/tex] is 225, which corresponds to option C.