College

We appreciate your visit to If tex f 3 191 5 tex when tex r 0 03 tex for the function tex f t P e rt tex then what. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

If [tex]f(3) = 191.5[/tex] when [tex]r = 0.03[/tex] for the function [tex]f(t) = P e^{rt}[/tex], then what is the approximate value of [tex]P[/tex]?

A. 78
B. 471
C. 175
D. 210

Answer :

To find the approximate value of [tex]\( P \)[/tex], we need to use the given function [tex]\( f(t) = P e^{rt} \)[/tex] and the provided information that [tex]\( f(3) = 191.5 \)[/tex] when [tex]\( r = 0.03 \)[/tex].

### Steps:

1. Understand the Problem:
- We have a function: [tex]\( f(t) = P e^{rt} \)[/tex].
- Given: [tex]\( f(3) = 191.5 \)[/tex], [tex]\( r = 0.03 \)[/tex].

2. Set Up the Equation:
- Substitute the given values into the equation:
[tex]\[
f(3) = P e^{0.03 \times 3}
\][/tex]
- This simplifies to:
[tex]\[
191.5 = P e^{0.09}
\][/tex]

3. Solve for [tex]\( P \)[/tex]:
- To find [tex]\( P \)[/tex], rearrange the equation:
[tex]\[
P = \frac{191.5}{e^{0.09}}
\][/tex]
- Calculate [tex]\( e^{0.09} \)[/tex] using a calculator. It’s approximately 1.09417.

4. Calculate [tex]\( P \)[/tex]:
- Plug this value back to find [tex]\( P \)[/tex]:
[tex]\[
P \approx \frac{191.5}{1.09417} \approx 175.02
\][/tex]

5. Round to a Provided Option:
- The closest value in the options provided is 175.

Thus, the approximate value of [tex]\( P \)[/tex] is 175. The correct answer is option C.

Thanks for taking the time to read If tex f 3 191 5 tex when tex r 0 03 tex for the function tex f t P e rt tex then what. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada