Answer :
Certainly! Let's solve this step-by-step:
We are given a function [tex]\( f(t) = P \cdot f^{\dagger} \)[/tex]. Based on the problem statement, the details about [tex]\( f^{\dagger} \)[/tex] are not explicitly provided. However, let's assume it represents a growth formula similar to compound interest: [tex]\( f(t) = P \cdot (1 + r)^t \)[/tex], where [tex]\( r \)[/tex] is the growth rate and [tex]\( t \)[/tex] is the time period.
We know:
- [tex]\( f(3) = 191.5 \)[/tex]
- [tex]\( r = 0.03 \)[/tex]
- [tex]\( t = 3 \)[/tex]
Our goal is to find the value of [tex]\( P \)[/tex].
1. Substitute the given values into the function:
[tex]\[
191.5 = P \cdot (1 + 0.03)^3
\][/tex]
2. Calculate the expression [tex]\( (1 + 0.03)^3 \)[/tex]:
[tex]\[
(1 + 0.03)^3 = 1.092727
\][/tex]
3. Use the equation from step 1 to solve for [tex]\( P \)[/tex]:
[tex]\[
191.5 = P \cdot 1.092727
\][/tex]
4. Solve for [tex]\( P \)[/tex] by dividing both sides by 1.092727:
[tex]\[
P = \frac{191.5}{1.092727} \approx 175.25
\][/tex]
Thus, the approximate value of [tex]\( P \)[/tex] is 175.25, which is closest to option B. So, the correct choice is:
B. 175
We are given a function [tex]\( f(t) = P \cdot f^{\dagger} \)[/tex]. Based on the problem statement, the details about [tex]\( f^{\dagger} \)[/tex] are not explicitly provided. However, let's assume it represents a growth formula similar to compound interest: [tex]\( f(t) = P \cdot (1 + r)^t \)[/tex], where [tex]\( r \)[/tex] is the growth rate and [tex]\( t \)[/tex] is the time period.
We know:
- [tex]\( f(3) = 191.5 \)[/tex]
- [tex]\( r = 0.03 \)[/tex]
- [tex]\( t = 3 \)[/tex]
Our goal is to find the value of [tex]\( P \)[/tex].
1. Substitute the given values into the function:
[tex]\[
191.5 = P \cdot (1 + 0.03)^3
\][/tex]
2. Calculate the expression [tex]\( (1 + 0.03)^3 \)[/tex]:
[tex]\[
(1 + 0.03)^3 = 1.092727
\][/tex]
3. Use the equation from step 1 to solve for [tex]\( P \)[/tex]:
[tex]\[
191.5 = P \cdot 1.092727
\][/tex]
4. Solve for [tex]\( P \)[/tex] by dividing both sides by 1.092727:
[tex]\[
P = \frac{191.5}{1.092727} \approx 175.25
\][/tex]
Thus, the approximate value of [tex]\( P \)[/tex] is 175.25, which is closest to option B. So, the correct choice is:
B. 175
