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Answer :
Let's solve the problem step by step.
We have a function [tex]\( f(t) = P \cdot e^{0.04t} \)[/tex], and we know that [tex]\( f(4) = 246.4 \)[/tex] when [tex]\( r = 0.04 \)[/tex]. We need to find the approximate value of [tex]\( P \)[/tex].
1. Set up the equation:
We are given that [tex]\( f(4) = 246.4 \)[/tex]. So, plug 4 into the function:
[tex]\[
f(4) = P \cdot e^{0.04 \cdot 4}
\][/tex]
Substitute the given value of [tex]\( f(4) \)[/tex]:
[tex]\[
246.4 = P \cdot e^{0.16}
\][/tex]
2. Calculate [tex]\( e^{0.16} \)[/tex]:
The exponential term [tex]\( e^{0.16} \)[/tex] is approximately 1.1735. This value comes from using a calculator or computing device.
3. Solve for [tex]\( P \)[/tex]:
With the equation [tex]\( 246.4 = P \cdot 1.1735 \)[/tex], solve for [tex]\( P \)[/tex]:
[tex]\[
P = \frac{246.4}{1.1735}
\][/tex]
4. Calculate the value of [tex]\( P \)[/tex]:
Performing the division, we find:
[tex]\[
P \approx 209.97
\][/tex]
5. Choose the closest answer:
Among the given options, 209.97 is approximately equal to 210.
Therefore, the approximate value of [tex]\( P \)[/tex] is [tex]\( 210 \)[/tex]. The correct answer is C. 210.
We have a function [tex]\( f(t) = P \cdot e^{0.04t} \)[/tex], and we know that [tex]\( f(4) = 246.4 \)[/tex] when [tex]\( r = 0.04 \)[/tex]. We need to find the approximate value of [tex]\( P \)[/tex].
1. Set up the equation:
We are given that [tex]\( f(4) = 246.4 \)[/tex]. So, plug 4 into the function:
[tex]\[
f(4) = P \cdot e^{0.04 \cdot 4}
\][/tex]
Substitute the given value of [tex]\( f(4) \)[/tex]:
[tex]\[
246.4 = P \cdot e^{0.16}
\][/tex]
2. Calculate [tex]\( e^{0.16} \)[/tex]:
The exponential term [tex]\( e^{0.16} \)[/tex] is approximately 1.1735. This value comes from using a calculator or computing device.
3. Solve for [tex]\( P \)[/tex]:
With the equation [tex]\( 246.4 = P \cdot 1.1735 \)[/tex], solve for [tex]\( P \)[/tex]:
[tex]\[
P = \frac{246.4}{1.1735}
\][/tex]
4. Calculate the value of [tex]\( P \)[/tex]:
Performing the division, we find:
[tex]\[
P \approx 209.97
\][/tex]
5. Choose the closest answer:
Among the given options, 209.97 is approximately equal to 210.
Therefore, the approximate value of [tex]\( P \)[/tex] is [tex]\( 210 \)[/tex]. The correct answer is C. 210.
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