Respuesta :

LammettHash

The equation is separable, so solving it is trivial:

[tex]\dfrac{\mathrm dy}{\mathrm dt}=ky\implies\dfrac{\mathrm dy}y=k\,\mathrm dt[/tex]

Integrating both sides gives

[tex]\ln|y|=kt+C\implies y=e^{kt+C}=Ce^{kt}[/tex]

Given [tex]y(0)=24[/tex] and [tex]y(1)=18[/tex], we find

[tex]24=C[/tex]

[tex]18=Ce^k=24e^k\implies e^k=\dfrac34\implies k=ln\dfrac34[/tex]

so the answer is E.

amna04352

Answer:

E

Step-by-step explanation:

dy/dt = ky

1/y .dy = k .dt

ln(y) = kt + c

t = 0, y = 24

ln(24) = 0 + c

c = ln(24)

ln(y) = kt + ln(24)

t = 1, y = 18

ln(18) = k + ln(24)

k = ln(18) - ln(24)

k = ln(18/24) = ln(3/4)

Otras preguntas