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Suppose $2000 is invested at 9% interest compounded continuously. How long will it take for the investment to grow to $10,000? Use the model A ( T ) = P e^rt and round to the nearest tenth of a year.

It will take approximately ____ years for the investment to grow to $10,000.
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Respuesta :

Answer:

7

Step-by-step explanation:

sing the equation         >    A  =  Pe^rt

20000  =    10000e^0.1t    >       10%  =  0.1

2  = e^0.1t

log 2  =    log e^0.1t               >     log to the base e

log 2  =  0.1t * 1              log e to the base e  =1

0.6931 = 0.1t

t =   6.931

  =    7 years

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