Chapter 4.5, Problem 55E

Breast Cancer It has been observed that the following formula accurately models the relationship between the size of a breast tumor and the amount of time that it has been growing. Vt=11001023e-0.02415t+1-4, where t is in months and Vt is measures in cubic centimeters. Source: Cancer. a. Find the tumor volume at 240 months. b. Assuming that the shape of a tumor is spherical, find the radius of the tumor from part a. Hint: The volume of a sphere is given by the formula V=4/3r3. c. If a tumor of size 0.5 cm3 is detected, according to the formula, how long has it been growing? What does this imply? d. Find limtVt and interpret this value. Explain whether this makes sense. e. Calculate the rate of change of tumor volume at 240 months and interpret.

Use the differential to approximate each quantity. Then use a calculator to approximate the quantity, and give the absolute value of the difference the two results to 4decimal places. 17.02

YOUR TURN Find dy if y=300x23,x=8, and dx=0.05.