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.
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.
