A very small tumor of initial size M is observed every ten days, and over each t

Question

A very small tumor of initial size M is observed every ten days, and over each ten-day period, it has grown 70% larger. (a) Write a formula representing the size of the tumor after t days (t = 0, 10, 20, . . .) S(t)= (b) On which day will we finally observe that the tumor is more than 10 times its original size? (Assume that the observations are strictly periodically conducted as specified.) day (C) How many times greater than its original size will the tumor be on day 100? (Round your answer to the nearest whole number.) times

Explanation / Answer

a) s(t) = M*(1+ (70/100))(t/10)

==> s(t) = M(1.7)(t/10)

b) 10M = M(1.7)(t/10)

==> (1.7)(t/10) = 10

applying natural log on both sides

==> ln (1.7)(t/10) = ln 10

==> (t/10) ln(1.7) = ln 10

==> t = 10 (ln 10)/(ln 1.7)

==> t = 10 (2.303)/(0.531)

==> t = 10(4.34)

==> t = 43.4

==> at 40th day tumor is 10 times initial size.

c) s(t) = M*(1.7)(t/10)

s(100) = M(1.7)(100/10)

==> s(100) = M(1.7)10

==> s(100) = M(201.6)

==> s(100) = 202M

Tumor is 202 times the initial size on 100th day

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.