Question

# 1) When interest is compounded continuously, the amount of money increases at a rate proportional to...

1) When interest is compounded continuously, the amount of money increases at a rate proportional to the amount S present at time t, that is,

dS/dt = rS, where r is the annual rate of interest.

(a)Find the amount of money accrued at the end of 9 years when \$4000 is deposited in a savings account drawing 5 1/4 \$ % annual interest compounded continuously. (Round your answer to the nearest cent.)

(b)In how many years will the initial sum deposited have doubled? (Round your answer to the nearest year.)

years

(c)Use a calculator to compare the amount obtained in part (a) with the amount S = 4000

(1 + 1/4 (0.0525)^9(4) that is accrued when interest is compounded quarterly. (Round your answer to the nearest cent.)

S = \$

2) The rate at which a body cools also depends on its exposed surface area S. If S is a constant, then a modification of (2), given in Section 3.1, is

dT/dt = kS(TTm), where k < 0 and Tm is a constant. Suppose that two cups A and B are filled with coffee at the same time. Initially, the temperature of the coffee is 160° F. The exposed surface area of the coffee in cup B is twice the surface area of the coffee in cup A. After 30 min the temperature of the coffee in cup A is 110° F. If

Tm = 80° F, then what is the temperature of the coffee in cup B after 30 min? (Round your answer to two decimal places.)
° F

BY THIS WAY, ANSWER OF GIVEN PROBLEM.

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