College

We appreciate your visit to If tex f 5 288 9 tex when tex r 0 05 tex for the function tex f t P e t 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(5)=288.9[/tex] when [tex]r=0.05[/tex] for the function [tex]f(t)=P e^t[/tex], then what is the approximate value of [tex]P[/tex]?

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

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

Thanks for taking the time to read If tex f 5 288 9 tex when tex r 0 05 tex for the function tex f t P e t 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