A model for the growth rate of tumor, known as the Gompertz Tumor Growth is given by the following equation: 9 (t) = 2-ee-" In 2 where g (t) is the growth rate of a tumor in mm /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 by integrating the function g (t) with respect to time t. Explain in your own words why this is so. (b) Use the symbols ty and t2 as the lower and upper bounds of the integral respectively. If ti is initialized as t = 0, calculate what will the value of t2 be? (c) Using your answer in part (b), write down the definite integral that will be used to calculate the volume (growth) of the tumor. (d) Solve the definite integral with an appropriate substitution. (e) State in English what the value of your answer in part (e) describes.
A model for the growth rate of tumor, known as the Gompertz Tumor Growth is given by the following equation: 9 (t) = 2-ee-" In 2 where g (t) is the growth rate of a tumor in mm /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 by integrating the function g (t) with respect to time t. Explain in your own words why this is so. (b) Use the symbols ty and t2 as the lower and upper bounds of the integral respectively. If ti is initialized as t = 0, calculate what will the value of t2 be? (c) Using your answer in part (b), write down the definite integral that will be used to calculate the volume (growth) of the tumor. (d) Solve the definite integral with an appropriate substitution. (e) State in English what the value of your answer in part (e) describes.
Chapter6: Exponential And Logarithmic Functions
Section6.1: Exponential Functions
Problem 60SE: The formula for the amount A in an investmentaccount with a nominal interest rate r at any timet is...
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Transcribed Image Text:A model for the growth rate of tumor, known as the Gompertz Tumor Growth is given by the following
equation:
g (t) = 21-ee- In 2
where g (t) is the growth rate of a tumor in mm3 /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 by integrating the function g (t) with respect to
time t. Explain in your own words why this is so.
(b) Use the symbols tį and t2 as the lower and upper bounds of the integral respectively. If ti is
initialized as ti = 0, calculate what will the value of t2 be?
(c) Using your answer in part (b), write down the definite integral that will be used to calculate the
volume (growth) of the tumor.
(d) Solve the definite integral with an appropriate substitution.
(e) State in English what the value of your answer in part (e) describes.
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