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Calculus Early Transcendentals 3rd Edition

Chemotherapy In an experimental study at Dartmouth College, mice with tumors were treated with the chemotherapeutic drug Cisplatin. Before treatment, the tumors consisted entirely of clonogenic cells that divide rapidly, causing the tumors to double in size every 2.9 days. Immediately after treatment, $99 \%$ of the cells in the tumor became quiescent cells which do not divide and lose $50 \%$ of their volume every 5.7 days. For a particular mouse, assume the tumor size is $0.5 \mathrm{cm}^{3}$ at the time of treatment.

a. Find an exponential decay function $V_{1}(t)$ that equals the total volume of the quiescent cells in the tumor $t$ days after treatment.

b. Find an exponential growth function $V_{2}(t)$ that equals the total volume of the clonogenic cells in the tumor $t$ days after treatment.

c. Use parts (a) and (b) to find a function $V(t)$ that equals the volume of the tumor $t$ days after treatment.

d. Plot a graph of $V(t)$ for $0 \leq t \leq 15 .$ What happens to the size of the tumor, assuming there are no follow-up treatments with Cisplatin?

e. In cases where more than one chemotherapy treatment is required, it is often best to give a second treatment just before the tumor starts growing again. For the mice in this exercise. when should the second treatment be given?