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 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!
Answer :
We are given the function
[tex]$$
f(t) = P e^{r t},
$$[/tex]
and the information that when [tex]$t = 3$[/tex] and [tex]$r = 0.03$[/tex], we have
[tex]$$
f(3) = 191.5.
$$[/tex]
This means that
[tex]$$
191.5 = P e^{0.03 \cdot 3}.
$$[/tex]
Since
[tex]$$
0.03 \cdot 3 = 0.09,
$$[/tex]
the equation becomes
[tex]$$
191.5 = P e^{0.09}.
$$[/tex]
To solve for [tex]$P$[/tex], we isolate it by dividing both sides by [tex]$e^{0.09}$[/tex]:
[tex]$$
P = \frac{191.5}{e^{0.09}}.
$$[/tex]
Evaluating [tex]$e^{0.09}$[/tex], we find that it is approximately [tex]$1.09417$[/tex]. Thus,
[tex]$$
P \approx \frac{191.5}{1.09417} \approx 175.
$$[/tex]
Therefore, the approximate value of [tex]$P$[/tex] is [tex]$\boxed{175}$[/tex], which corresponds to option C.
[tex]$$
f(t) = P e^{r t},
$$[/tex]
and the information that when [tex]$t = 3$[/tex] and [tex]$r = 0.03$[/tex], we have
[tex]$$
f(3) = 191.5.
$$[/tex]
This means that
[tex]$$
191.5 = P e^{0.03 \cdot 3}.
$$[/tex]
Since
[tex]$$
0.03 \cdot 3 = 0.09,
$$[/tex]
the equation becomes
[tex]$$
191.5 = P e^{0.09}.
$$[/tex]
To solve for [tex]$P$[/tex], we isolate it by dividing both sides by [tex]$e^{0.09}$[/tex]:
[tex]$$
P = \frac{191.5}{e^{0.09}}.
$$[/tex]
Evaluating [tex]$e^{0.09}$[/tex], we find that it is approximately [tex]$1.09417$[/tex]. Thus,
[tex]$$
P \approx \frac{191.5}{1.09417} \approx 175.
$$[/tex]
Therefore, the approximate value of [tex]$P$[/tex] is [tex]$\boxed{175}$[/tex], which corresponds to 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 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!
- 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
