College

Dear beloved readers, welcome to our website! We hope your visit here brings you valuable insights and meaningful inspiration. Thank you for taking the time to stop by and explore the content we've prepared for you.
------------------------------------------------ If [tex]f(4) = 246.4[/tex] when [tex]r = 0.04[/tex] for the function [tex]f(t) = Pe^{rt}[/tex], then what is the approximate value of [tex]P[/tex]?

A. 1220
B. 50
C. 289
D. 210

Answer :

To find the approximate value of [tex]\( P \)[/tex] in the function [tex]\( f(t) = P \cdot e^{rt} \)[/tex], where [tex]\( f(4) = 246.4 \)[/tex] and [tex]\( r = 0.04 \)[/tex], we can follow these steps:

1. We know the equation is [tex]\( f(t) = P \cdot e^{rt} \)[/tex]. Plugging in the values we have:
[tex]\[
246.4 = P \cdot e^{0.04 \cdot 4}
\][/tex]

2. Calculate the exponent:
[tex]\[
rt = 0.04 \cdot 4 = 0.16
\][/tex]

3. Compute [tex]\( e^{0.16} \)[/tex], which is approximately 1.1735.

4. Now, substitute the value of [tex]\( e^{0.16} \)[/tex] back into the equation:
[tex]\[
246.4 = P \cdot 1.1735
\][/tex]

5. Solve for [tex]\( P \)[/tex] by dividing both sides of the equation by 1.1735:
[tex]\[
P = \frac{246.4}{1.1735} \approx 210
\][/tex]

Thus, the approximate value of [tex]\( P \)[/tex] is 210, which corresponds to option D.