We appreciate your visit to If tex f 5 288 9 tex when tex r 0 05 tex for the function tex f t Pe rt tex then what is. 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!
Answer :
To solve this problem, we need to find the value of [tex]\( P \)[/tex] in the function [tex]\( f(t) = P \cdot e^{rt} \)[/tex], given that [tex]\( f(5) = 288.9 \)[/tex] and [tex]\( r = 0.05 \)[/tex].
Let's break this down step-by-step:
1. Identify the equation: The function is given as [tex]\( f(t) = P \cdot e^{rt} \)[/tex].
2. Substitute the known values: We know [tex]\( f(5) = 288.9 \)[/tex], [tex]\( r = 0.05 \)[/tex], and [tex]\( t = 5 \)[/tex]. So, we substitute these into the equation:
[tex]\[
288.9 = P \cdot e^{0.05 \times 5}
\][/tex]
3. Simplify the exponent: Calculate the expression within the exponent:
[tex]\[
0.05 \times 5 = 0.25
\][/tex]
Thus, the equation becomes:
[tex]\[
288.9 = P \cdot e^{0.25}
\][/tex]
4. Calculate [tex]\( e^{0.25} \)[/tex]: The value of [tex]\( e^{0.25} \)[/tex] is approximately 1.284.
5. Solve for [tex]\( P \)[/tex]: Rearrange the equation to solve for [tex]\( P \)[/tex]:
[tex]\[
P = \frac{288.9}{e^{0.25}}
\][/tex]
[tex]\[
P = \frac{288.9}{1.284}
\][/tex]
6. Calculate [tex]\( P \)[/tex]: Dividing gives us an approximate value of:
[tex]\[
P \approx 225
\][/tex]
From the options given, the closest approximate value is [tex]\( \boxed{225} \)[/tex].
Let's break this down step-by-step:
1. Identify the equation: The function is given as [tex]\( f(t) = P \cdot e^{rt} \)[/tex].
2. Substitute the known values: We know [tex]\( f(5) = 288.9 \)[/tex], [tex]\( r = 0.05 \)[/tex], and [tex]\( t = 5 \)[/tex]. So, we substitute these into the equation:
[tex]\[
288.9 = P \cdot e^{0.05 \times 5}
\][/tex]
3. Simplify the exponent: Calculate the expression within the exponent:
[tex]\[
0.05 \times 5 = 0.25
\][/tex]
Thus, the equation becomes:
[tex]\[
288.9 = P \cdot e^{0.25}
\][/tex]
4. Calculate [tex]\( e^{0.25} \)[/tex]: The value of [tex]\( e^{0.25} \)[/tex] is approximately 1.284.
5. Solve for [tex]\( P \)[/tex]: Rearrange the equation to solve for [tex]\( P \)[/tex]:
[tex]\[
P = \frac{288.9}{e^{0.25}}
\][/tex]
[tex]\[
P = \frac{288.9}{1.284}
\][/tex]
6. Calculate [tex]\( P \)[/tex]: Dividing gives us an approximate value of:
[tex]\[
P \approx 225
\][/tex]
From the options given, the closest approximate value is [tex]\( \boxed{225} \)[/tex].
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 Pe rt tex then what is. 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!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
