Answer :
Sure, let's solve the problem step by step.
We are given a function [tex]\( f(t) = P \cdot e^{rt} \)[/tex], where the values for [tex]\( f(5) \)[/tex], [tex]\( r \)[/tex], and [tex]\( t \)[/tex] are provided. We need to find the approximate value of [tex]\( P \)[/tex].
Here's what we know:
- [tex]\( f(5) = 288.9 \)[/tex]
- [tex]\( r = 0.05 \)[/tex]
- [tex]\( t = 5 \)[/tex]
The function we have is:
[tex]\[ f(t) = P \cdot e^{rt} \][/tex]
Substituting the given values into the function gives us:
[tex]\[ 288.9 = P \cdot e^{0.05 \times 5} \][/tex]
First, let's calculate the exponent:
[tex]\[ 0.05 \times 5 = 0.25 \][/tex]
Next, find [tex]\( e^{0.25} \)[/tex].
Using the calculated value for the exponential part:
[tex]\[ e^{0.25} \approx 1.284 \][/tex]
Now, we substitute this back into the equation:
[tex]\[ 288.9 = P \cdot 1.284 \][/tex]
To solve for [tex]\( P \)[/tex], divide both sides of the equation by 1.284:
[tex]\[ P = \frac{288.9}{1.284} \][/tex]
[tex]\[ P \approx 225 \][/tex]
Therefore, the approximate value of [tex]\( P \)[/tex] is 225.
So the correct answer is B. 225.
We are given a function [tex]\( f(t) = P \cdot e^{rt} \)[/tex], where the values for [tex]\( f(5) \)[/tex], [tex]\( r \)[/tex], and [tex]\( t \)[/tex] are provided. We need to find the approximate value of [tex]\( P \)[/tex].
Here's what we know:
- [tex]\( f(5) = 288.9 \)[/tex]
- [tex]\( r = 0.05 \)[/tex]
- [tex]\( t = 5 \)[/tex]
The function we have is:
[tex]\[ f(t) = P \cdot e^{rt} \][/tex]
Substituting the given values into the function gives us:
[tex]\[ 288.9 = P \cdot e^{0.05 \times 5} \][/tex]
First, let's calculate the exponent:
[tex]\[ 0.05 \times 5 = 0.25 \][/tex]
Next, find [tex]\( e^{0.25} \)[/tex].
Using the calculated value for the exponential part:
[tex]\[ e^{0.25} \approx 1.284 \][/tex]
Now, we substitute this back into the equation:
[tex]\[ 288.9 = P \cdot 1.284 \][/tex]
To solve for [tex]\( P \)[/tex], divide both sides of the equation by 1.284:
[tex]\[ P = \frac{288.9}{1.284} \][/tex]
[tex]\[ P \approx 225 \][/tex]
Therefore, the approximate value of [tex]\( P \)[/tex] is 225.
So the correct answer is B. 225.
