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A 2005 study by the fisheries research services in aberdeen, scotland, suggests that the average length of the species clupea harengus (atlantic herring) as a function of age t (in years) can be modeled by l(t) = 32(1 − e−0.37t) cm for 0 ≤ t ≤ 13. how fast is the length changing at age t = 7 years?

Respuesta :

The length at time t is modeled as
[tex]L(t)=32(1-e^{-0.37t} ) \, cm, \,\, 0\le t \le 13[/tex]

The rate of change of the length is
[tex] \frac{dL}{dt} = -0.37(32)e^{-0.37t} = -11.84e^{-0.37t}[/tex]

When t = 7 years,
[tex] \frac{dL}{dt}|_{t=7} =-11.84e^{-0.37 \times 7} = -0.8882 \,\, cm/yr[/tex]

Answer: -0.8882 cm/year

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