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2. Gompertz Tumor Growth [13] A model for the growth rate of tumor, known as the Gompertz Tumor Growth is given by the following equation: \[ g(t)=2^{1-e^{-t}} e^{-t} \ln 2 \] where \( g(t) \) is the grouth rate of a \( t \) mor in \( \mathrm{mm}^{3} / \) month and \( t \) is the time in months. By how much is the volume of the tumor predicted to increase over the first year? Solve the above, by answering the following questions: (a) The volume (growth) of the tumor can be found bu futegrating the function \( g(t) \) with respect to time \( t \). Explain in your own words why this is so.|3| b) Use the symbols \( t_{1} \) and \( t_{2} \) as the lower and upper bolmds of the integral respectively. If \( t_{1} \) is initialized as \( t_{1}=0 \), calculate what will the value of \( t_{2} \) be? \( |1| \) C) ''sing Jom answer in prat (b), write down the defimile integral that will be used to calculate the volume (growth) of the tumor.|1| d) Solve the definite integral with an appropriate substitution. \( |6| \) (e) State in English what the value of your answer in part (e) describ

          2. Gompertz Tumor Growth [13]
A model for the growth rate of tumor, known as the Gompertz Tumor Growth is given by the following equation:
\[
g(t)=2^{1-e^{-t}} e^{-t} \ln 2
\]
where \( g(t) \) is the grouth rate of a \( t \) mor in \( \mathrm{mm}^{3} / \) month and \( t \) is the time in months. By how much is the volume of the tumor predicted to increase over the first year?
Solve the above, by answering the following questions:
(a) The volume (growth) of the tumor can be found bu futegrating the function \( g(t) \) with respect to time \( t \). Explain in your own words why this is so.|3|
b) Use the symbols \( t_{1} \) and \( t_{2} \) as the lower and upper bolmds of the integral respectively. If \( t_{1} \) is initialized as \( t_{1}=0 \), calculate what will the value of \( t_{2} \) be? \( |1| \)
C) ''sing Jom answer in prat (b), write down the defimile integral that will be used to calculate the volume (growth) of the tumor.|1|
d) Solve the definite integral with an appropriate substitution. \( |6| \)
(e) State in English what the value of your answer in part (e) describ

2. Gompertz Tumor Growth [13]
A model for the growth rate of tumor, known as the Gompertz Tumor Growth is given by the following equation:

g(t)=2^1-e^-t e^-tln 2

where g(t) is the grouth rate of a t mor in mm^3 / month and t is the time in months. By how much is the volume of the tumor predicted to increase over the first year?
Solve the above, by answering the following questions:
(a) The volume (growth) of the tumor can be found bu futegrating the function g(t) with respect to time t. Explain in your own words why this is so.|3|
b) Use the symbols t1 and t2 as the lower and upper bolmds of the integral respectively. If t1 is initialized as t1=0, calculate what will the value of t2 be? |1|
C) ”sing Jom answer in prat (b), write down the defimile integral that will be used to calculate the volume (growth) of the tumor.|1|
d) Solve the definite integral with an appropriate substitution. |6|
(e) State in English what the value of your answer in part (e) describ

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