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Answer :
Sure, let's solve the problem step-by-step using the information provided.
We are given the function:
[tex]\[ f(t) = P \cdot e^{r \cdot t} \][/tex]
where [tex]\( f(5) = 288.9 \)[/tex], [tex]\( r = 0.05 \)[/tex], and [tex]\( t = 5 \)[/tex].
We need to find the value of [tex]\( P \)[/tex].
1. First, plug the known values into the equation:
[tex]\[ 288.9 = P \cdot e^{0.05 \cdot 5} \][/tex]
2. Simplify the exponent:
[tex]\[ e^{0.25} \][/tex]
3. Solve for [tex]\( P \)[/tex] by rearranging the equation:
[tex]\[ P = \frac{288.9}{e^{0.25}} \][/tex]
4. Calculate [tex]\( e^{0.25} \)[/tex]. The approximate value of [tex]\( e^{0.25} \)[/tex] is 1.2840.
5. Now, divide 288.9 by 1.2840 to find [tex]\( P \)[/tex]:
[tex]\[ P \approx \frac{288.9}{1.2840} \approx 225 \][/tex]
Therefore, the approximate value of [tex]\( P \)[/tex] is 225.
The correct answer is C. 225.
We are given the function:
[tex]\[ f(t) = P \cdot e^{r \cdot t} \][/tex]
where [tex]\( f(5) = 288.9 \)[/tex], [tex]\( r = 0.05 \)[/tex], and [tex]\( t = 5 \)[/tex].
We need to find the value of [tex]\( P \)[/tex].
1. First, plug the known values into the equation:
[tex]\[ 288.9 = P \cdot e^{0.05 \cdot 5} \][/tex]
2. Simplify the exponent:
[tex]\[ e^{0.25} \][/tex]
3. Solve for [tex]\( P \)[/tex] by rearranging the equation:
[tex]\[ P = \frac{288.9}{e^{0.25}} \][/tex]
4. Calculate [tex]\( e^{0.25} \)[/tex]. The approximate value of [tex]\( e^{0.25} \)[/tex] is 1.2840.
5. Now, divide 288.9 by 1.2840 to find [tex]\( P \)[/tex]:
[tex]\[ P \approx \frac{288.9}{1.2840} \approx 225 \][/tex]
Therefore, the approximate value of [tex]\( P \)[/tex] is 225.
The correct answer is C. 225.
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