Respuesta :
Answer:
8 years
Step-by-step explanation:
An initial investment of $100 is now valued at $150. The annual interest rate is 5%, compounded continuously. The equation [tex]100e^{0.05t} = 150[/tex] represents the situation, where t is the number of years the money has been invested.
To find out how long has the money invested we need to find out 't'
[tex]100e^{0.05t} = 150[/tex] , solve for t
divide both sides by 100
[tex]e^{0.05t} = 1.5[/tex]
Now to remove 'e' we take ln on both sides
[tex]ln(e^{0.05t) = ln 1.5[/tex]
the value of [tex]ln(e)= 1[/tex]
[tex]0.05t = ln 1.5[/tex]
Now divide by 0.05 on both sides
t = 8.10930
The money is invested for 8 years
