Answer :
Let's solve the problem step-by-step to find the approximate value of [tex]\( P \)[/tex].
We are given the function [tex]\( f(t) = P \cdot e^{rt} \)[/tex] and specific values: [tex]\( f(4) = 246.4 \)[/tex] and [tex]\( r = 0.04 \)[/tex].
To find [tex]\( P \)[/tex], we can use the equation for the function at [tex]\( t = 4 \)[/tex]:
[tex]\[ f(4) = P \cdot e^{0.04 \times 4} \][/tex]
Substitute the given value of [tex]\( f(4) \)[/tex]:
[tex]\[ 246.4 = P \cdot e^{0.16} \][/tex]
To solve for [tex]\( P \)[/tex], we rearrange the equation to:
[tex]\[ P = \frac{246.4}{e^{0.16}} \][/tex]
Now, we need the value of [tex]\( e^{0.16} \)[/tex]. Let's say [tex]\( e^{0.16} \approx 1.1735 \)[/tex].
Substituting this into the equation:
[tex]\[ P = \frac{246.4}{1.1735} \][/tex]
Perform the division:
[tex]\[ P \approx 209.97 \][/tex]
This result is approximately 210 when rounded to the nearest integer. Therefore, the approximate value of [tex]\( P \)[/tex] is:
B. 210
We are given the function [tex]\( f(t) = P \cdot e^{rt} \)[/tex] and specific values: [tex]\( f(4) = 246.4 \)[/tex] and [tex]\( r = 0.04 \)[/tex].
To find [tex]\( P \)[/tex], we can use the equation for the function at [tex]\( t = 4 \)[/tex]:
[tex]\[ f(4) = P \cdot e^{0.04 \times 4} \][/tex]
Substitute the given value of [tex]\( f(4) \)[/tex]:
[tex]\[ 246.4 = P \cdot e^{0.16} \][/tex]
To solve for [tex]\( P \)[/tex], we rearrange the equation to:
[tex]\[ P = \frac{246.4}{e^{0.16}} \][/tex]
Now, we need the value of [tex]\( e^{0.16} \)[/tex]. Let's say [tex]\( e^{0.16} \approx 1.1735 \)[/tex].
Substituting this into the equation:
[tex]\[ P = \frac{246.4}{1.1735} \][/tex]
Perform the division:
[tex]\[ P \approx 209.97 \][/tex]
This result is approximately 210 when rounded to the nearest integer. Therefore, the approximate value of [tex]\( P \)[/tex] is:
B. 210
