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(3)=191.5[/tex] when [tex]r=0.03[/tex] for the function [tex]f(t)=P e^{rt}[/tex], then what is the approximate value of [tex]P[/tex]?

A. 471
B. 78
C. 175
D. 210

Answer :

We are given the function

[tex]$$
f(t) = P\, e^{rt}
$$[/tex]

with [tex]$r = 0.03$[/tex]. Also, it is known that

[tex]$$
f(3) = 191.5.
$$[/tex]

This means that

[tex]$$
191.5 = P\, e^{0.03 \times 3}.
$$[/tex]

Step 1. Calculate the exponent:
[tex]$$
0.03 \times 3 = 0.09.
$$[/tex]

Step 2. Substitute the value back into the equation:
[tex]$$
191.5 = P\, e^{0.09}.
$$[/tex]

Step 3. Solve for [tex]$P$[/tex] by isolating it:
[tex]$$
P = \frac{191.5}{e^{0.09}}.
$$[/tex]

Step 4. Using the approximation [tex]$e^{0.09}\approx 1.09417$[/tex], we compute

[tex]$$
P \approx \frac{191.5}{1.09417} \approx 175.
$$[/tex]

Thus, the approximate value of [tex]$P$[/tex] is [tex]$\boxed{175}$[/tex], which corresponds to option C.