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 9.2 9.8 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 Transform the data correctly to perform a linear least-squares regression, then report your model as y=cekxy=cekx. Estimate the catastrophe rate when the microtubule is 0.30 of the cell half-length.
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 9.2 9.8 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 Transform the data correctly to perform a linear least-squares regression, then report your model as y=cekxy=cekx. Estimate the catastrophe rate when the microtubule is 0.30 of the cell half-length.
Chapter6: Exponential And Logarithmic Functions
Section6.8: Fitting Exponential Models To Data
Problem 3TI: Table 6 shows the population, in thousands, of harbor seals in the Wadden Sea over the years 1997 to...
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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 | 9.2 | 9.8 |
| 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 |
Transform the data correctly to perform a linear least-squares regression, then report your model as y=cekxy=cekx. Estimate the catastrophe rate when the microtubule is 0.30 of the cell half-length.
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