+99 Melissa invested $500 in a savings account the pays an annual interest rate of 3.5% compounded continuously. How long will it take for her savings to reach $650.
I know this uses the A=Pe^rt formula but I only know P=500, r=3.5, A=650... If I am right, there are still ones which I don't know.
Please explain how to solve this. thankyou :) <3
Solve for t over the real numbers:
650 = 500 e^(0.035 t)
500 e^(0.035 t) = 500 e^(7 t/200):
650 = 500 e^((7 t)/200)
650 = 500 e^((7 t)/200) is equivalent to 500 e^((7 t)/200) = 650:
500 e^((7 t)/200) = 650
Divide both sides by 500:
e^((7 t)/200) = 13/10
Take the natural logarithm of both sides:
(7 t)/200 = log(13/10)
Multiply both sides by 200/7:
Answer: | t = 200/7 log(13/10)=7.50 Years.
+99 Ah, I just remembered e = 2.718
Whoever considered solving this, how nice of you 
<3 thankyou, there's no need to solve it anymore~ I just understood it
Solve for t over the real numbers:
650 = 500 e^(0.035 t)
500 e^(0.035 t) = 500 e^(7 t/200):
650 = 500 e^((7 t)/200)
650 = 500 e^((7 t)/200) is equivalent to 500 e^((7 t)/200) = 650:
500 e^((7 t)/200) = 650
Divide both sides by 500:
e^((7 t)/200) = 13/10
Take the natural logarithm of both sides:
(7 t)/200 = log(13/10)
Multiply both sides by 200/7:
Answer: | t = 200/7 log(13/10)=7.50 Years.
