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
