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The growth of malignant tumors can be modeled using the Gompertz model. dP = r.P. In in) dt where r> 0 is the intrinsic growth rate and K > 0 is a constant. a) Find the general solution to the Gompertz model and state the significance of the constant K. b) A tumor with 2,500 cells is initially growing at a rate of 500 cells/day. Assuming the maximum size of the tumor is 100,000 cells, how large will the tumor be after 50 days?

The growth of malignant tumors can be modeled using the Gompertz model. dP = r.P. In in) dt where r> 0 is the intrinsic growth rate and K > 0 is a constant. a) Find the general solution to the Gompertz model and state the significance of the constant K. b) A tumor with 2,500 cells is initially growing at a rate of 500 cells/day. Assuming the maximum size of the tumor is 100,000 cells, how large will the tumor be after 50 days?

Advanced Engineering Mathematics
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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The growth of malignant tumors can be modeled using the Gompertz model. dP = r.P. In dt where r> 0 is the intrinsic growth rate and K > O is a constant. a) Find the general solution to the Gompertz model and state the significance of the constant K. b) A tumor with 2,500 cells is initially growing at a rate of 500 cells/day. Assuming the maximum size of the tumor is 100,000 cells, how large will the tumor be after 50 days?
Transcribed Image Text:The growth of malignant tumors can be modeled using the Gompertz model. dP = r.P. In dt where r> 0 is the intrinsic growth rate and K > O is a constant. a) Find the general solution to the Gompertz model and state the significance of the constant K. b) A tumor with 2,500 cells is initially growing at a rate of 500 cells/day. Assuming the maximum size of the tumor is 100,000 cells, how large will the tumor be after 50 days?
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