5.(Inspiration drawn from Vilela et al 2010) Microtubules are tubular structures in the cytoplasm of cells that can elongate and form more complex structures but can undergo catastrophic collapse as they get longer within the cell. Suppose the rate of catastrophe (per minute) was thought to be an exponential model of relative length of the microtubules (fraction of cell half-length) based on the following data:Fraction of Cell Half-Length0.210.280.340.420.470.520.550.590.620.710.790.810.850.920.98Catastrophe Rate0.10530.13440.14860.17030.19000.21100.21820.23310.25570.29900.34760.35870.38320.43710.4819 Transform the data correctly to perform a linear least-squares regression, then report your model as y = cecek.Estimate the catastrophe rate when the microtubule is 0.30 of the cell half-length.

Answered: (Inspiration drawn from Vilela et al…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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(Inspiration drawn from Vilela et al 2010) Microtubules are tubular structures in the cytoplasm of cells that can elongate and form more complex structures but can undergo catastrophic collapse as they get longer within the cell. Suppose the rate of catastrophe (per minute) was thought to be an exponential model of relative length of the microtubules (fraction of cell half-length) based on the following data:

Fraction of Cell Half-Length	0.21	0.28	0.34	0.42	0.47	0.52	0.55	0.59	0.62	0.71	0.79	0.81	0.85	0.92	0.98
Catastrophe Rate	0.1053	0.1344	0.1486	0.1703	0.1900	0.2110	0.2182	0.2331	0.2557	0.2990	0.3476	0.3587	0.3832	0.4371	0.4819