match each function described on the left with an ordered pair that is a solution to the function. round to…

1. Recall the formula for continuous - compounding:
   • The formula for continuous - compounding is $A = Pe^{rt}$, where $A$ is the final amount, $P$ is the principal amount (initial investment), $r$ is the annual interest rate (in decimal form), and $t$ is the time in years.
2. Analyze the first investment:
   • For an initial investment of $P = 500$ and $r=0.03$. When $t = 10$, $A = 500e^{0.03\times10}=500e^{0.3}$.
     • Calculate $e^{0.3}\approx1.34986$. Then $A = 500\times1.34986 = 674.93$.
3. Analyze the second investment:
   • For an initial investment of $P = 300$ and $r = 0.05$. When $t = 10$, $A=300e^{0.05\times10}=300e^{0.5}$.
     • Calculate $e^{0.5}\approx1.64872$. Then $A = 300\times1.64872=494.62$.
4. Analyze the third investment:
   • For an initial investment of $P = 600$ and $r = 0.02$. When $t = 10$, $A = 600e^{0.02\times10}=600e^{0.2}$.
     • Calculate $e^{0.2}\approx1.22140$. Then $A = 600\times1.22140 = 732.84$. So the ordered - pair $(10,732.84)$ corresponds to an initial investment of $$600$ earning $2%$ interest compounded continuously.
5. Analyze the fourth investment:
   • For an initial investment of $P = 200$ and $r = 0.06$. When $t = 0$, $A = 200e^{0.06\times0}=200\times1 = 200$. So the ordered - pair $(0,200)$ corresponds to an initial investment of $$200$ earning $6%$ interest compounded continuously.

Answer:

• An initial investment of $$500$ earning $3%$ interest compounded continuously: No match given.
• An initial investment of $$300$ earning $5%$ interest compounded continuously: No match given.
• An initial investment of $$600$ earning $2%$ interest compounded continuously: $(10,732.84)$
• An initial investment of $$200$ earning $6%$ interest compounded continuously: $(0,200)$