Westonci.ca is your go-to source for answers, with a community ready to provide accurate and timely information. Connect with a community of experts ready to provide precise solutions to your questions on our user-friendly Q&A platform. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.
Sagot :
To solve for the function [tex]\( f(t) = P e^{r t} \)[/tex], given [tex]\( P = 7 \)[/tex] and [tex]\( r = 0.07 \)[/tex], we need to determine the value of [tex]\( f(7) \)[/tex] to the nearest tenth.
Let's break it down step by step:
1. Identify the given values:
- [tex]\( P = 7 \)[/tex]
- [tex]\( r = 0.07 \)[/tex]
- [tex]\( t = 7 \)[/tex]
2. Substitute the values into the function [tex]\( f(t) = P e^{r t} \)[/tex]:
[tex]\[ f(7) = 7 \cdot e^{0.07 \cdot 7} \][/tex]
3. Calculate the exponent [tex]\( 0.07 \cdot 7 \)[/tex]:
[tex]\[ 0.07 \cdot 7 = 0.49 \][/tex]
4. Find the value of [tex]\( e^{0.49} \)[/tex]:
We know the base of the natural logarithm, [tex]\( e \)[/tex], is approximately 2.71828. Evaluating [tex]\( e^{0.49} \)[/tex]:
[tex]\[ e^{0.49} \approx 1.63231 \][/tex]
5. Multiply this result by 7:
[tex]\[ 7 \cdot 1.63231 \approx 11.426213539687653 \][/tex]
6. Round this value to the nearest tenth:
[tex]\[ 11.426213539687653 \approx 11.4 \][/tex]
Therefore, the value of [tex]\( f(7) \)[/tex] to the nearest tenth is [tex]\( 11.4 \)[/tex].
The correct answer is:
D. 11.4
Let's break it down step by step:
1. Identify the given values:
- [tex]\( P = 7 \)[/tex]
- [tex]\( r = 0.07 \)[/tex]
- [tex]\( t = 7 \)[/tex]
2. Substitute the values into the function [tex]\( f(t) = P e^{r t} \)[/tex]:
[tex]\[ f(7) = 7 \cdot e^{0.07 \cdot 7} \][/tex]
3. Calculate the exponent [tex]\( 0.07 \cdot 7 \)[/tex]:
[tex]\[ 0.07 \cdot 7 = 0.49 \][/tex]
4. Find the value of [tex]\( e^{0.49} \)[/tex]:
We know the base of the natural logarithm, [tex]\( e \)[/tex], is approximately 2.71828. Evaluating [tex]\( e^{0.49} \)[/tex]:
[tex]\[ e^{0.49} \approx 1.63231 \][/tex]
5. Multiply this result by 7:
[tex]\[ 7 \cdot 1.63231 \approx 11.426213539687653 \][/tex]
6. Round this value to the nearest tenth:
[tex]\[ 11.426213539687653 \approx 11.4 \][/tex]
Therefore, the value of [tex]\( f(7) \)[/tex] to the nearest tenth is [tex]\( 11.4 \)[/tex].
The correct answer is:
D. 11.4
Thank you for choosing our service. We're dedicated to providing the best answers for all your questions. Visit us again. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.