contestada

use guess and check to find when an exponential function with a decay rate of 15% per hour reaches half of its original amount, rounded up to the nearest hour. The exponential function reaches half of itsoriginal amount after how many hours?

Respuesta :

Answer:

1.386 or 1 hour

Step-by-step explanation:

Given that decay rate is 15% per hour.

i.e. y' =-0.15y

Separate the variables and integrate

ln y =-0.15 t +C where t = no of hours

Or [tex]y =Ae^{-0.5t}[/tex] where A = initial amount present

When it becomes 1/2 A we have

[tex]A/2 =Ae^{-0.5t}[/tex]

Or [tex]1/2 =e^{-0.5t}[/tex]

[tex]ln(1/2) ={-0.5t}[/tex]

=1.386

In other words in 1 hour (after rounding off) the exponential function reaches its half.

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