We appreciate your visit to Question 1 of 10 Exponential GrowthIf tex f 3 191 5 tex when tex r 0 03 tex for the function tex f t P. 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 find the approximate value of [tex]\( P \)[/tex] in the given exponential function [tex]\( f(i) = P \times e^{-r \times i} \)[/tex], we are provided with some values:
- [tex]\( f(3) = 191.5 \)[/tex]
- [tex]\( r = 0.03 \)[/tex]
- [tex]\( i = 3 \)[/tex]
The function can be expressed as:
[tex]\[ f(i) = P \times e^{-r \times i} \][/tex]
We need to find [tex]\( P \)[/tex] when [tex]\( f(3) = 191.5 \)[/tex]. This requires us to rearrange the equation to solve for [tex]\( P \)[/tex].
1. Start with the equation given:
[tex]\[ f(3) = P \times e^{-0.03 \times 3} \][/tex]
2. Substitute the known value of [tex]\( f(3) \)[/tex]:
[tex]\[ 191.5 = P \times e^{-0.09} \][/tex]
3. Calculate the value of [tex]\( e^{-0.09} \)[/tex]. Using a calculator, [tex]\( e^{-0.09} \approx 0.9139 \)[/tex].
4. Substitute this back into the equation:
[tex]\[ 191.5 = P \times 0.9139 \][/tex]
5. Now, solve for [tex]\( P \)[/tex] by dividing both sides by 0.9139:
[tex]\[ P = \frac{191.5}{0.9139} \][/tex]
6. Performing the division gives:
[tex]\[ P \approx 209.53 \][/tex]
Therefore, the approximate value of [tex]\( P \)[/tex] is closest to option C, which is 210.
- [tex]\( f(3) = 191.5 \)[/tex]
- [tex]\( r = 0.03 \)[/tex]
- [tex]\( i = 3 \)[/tex]
The function can be expressed as:
[tex]\[ f(i) = P \times e^{-r \times i} \][/tex]
We need to find [tex]\( P \)[/tex] when [tex]\( f(3) = 191.5 \)[/tex]. This requires us to rearrange the equation to solve for [tex]\( P \)[/tex].
1. Start with the equation given:
[tex]\[ f(3) = P \times e^{-0.03 \times 3} \][/tex]
2. Substitute the known value of [tex]\( f(3) \)[/tex]:
[tex]\[ 191.5 = P \times e^{-0.09} \][/tex]
3. Calculate the value of [tex]\( e^{-0.09} \)[/tex]. Using a calculator, [tex]\( e^{-0.09} \approx 0.9139 \)[/tex].
4. Substitute this back into the equation:
[tex]\[ 191.5 = P \times 0.9139 \][/tex]
5. Now, solve for [tex]\( P \)[/tex] by dividing both sides by 0.9139:
[tex]\[ P = \frac{191.5}{0.9139} \][/tex]
6. Performing the division gives:
[tex]\[ P \approx 209.53 \][/tex]
Therefore, the approximate value of [tex]\( P \)[/tex] is closest to option C, which is 210.
Thanks for taking the time to read Question 1 of 10 Exponential GrowthIf tex f 3 191 5 tex when tex r 0 03 tex for the function tex f t P. 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
