(Solved): The rate of proliferation (that is, reproduction) for the cells in a tumor varies depending on the ...

The rate of proliferation (that is, reproduction) for the cells in a tumor varies depending on the size of the tumor. The Gompertz growth model is sometimes used to model this growth. According to the Gompertz model the total number of divisions occurring in 1 hour, R, depends on the number of cells, $\mathrm{N}$, through the formula given below. $\mathrm{R}(\mathrm{N})=\mathrm{dN}\ln \left(\frac{\mathrm{A}}{\mathrm{N}}\right)$ The positive constants, $\mathrm{d}$ and $\mathrm{A}$, both depend on the type of tumor, whether it is being treated or not, and so on. (a) Assume that $d=A=1$. Use a table or a graph to show that ${\lim }_{N?0}R(N)=0$. Complete the table of values to show that ${\lim }_{\mathrm{N}?0}\mathrm{R}(\mathrm{N})=0$. (Type an integer or decimal rounded to three decimal places as needed.) (b) The per cell rate of reproduction tells us how many times any cell in the tumor will divide in one hour. It is given by $r(N)=\frac{R(N)}{N}$. Show that lim $N?0r(N)$ does not exist (again assume that $d=A=1$ ). The following graph of $r(N)$ shows that ${\lim }_{N?0}r(N)$ does not exist. Select the correct graph below.