Math 1324 Business Algebra

Canvas Exercise Set 13&14

Instructor : Byungik "Ike" Kahng

Date:

Student Name:

1. Compound Interest Model

Recall that you invest a principal of P with annual interest rate r compounded n times a year. Then, the balance

after t years under this discrete compounding scheme is as follows.

B(t) = P 1+ r

n  n t.

Typically, n = 12 (monthly reinvestment) or n = 4 (quarterly reinvestment) for most consumer accounts.

Bank A offers an investment CD with an annual interest rate of 5.1% compounded monthly, that of bank B offers has

an annual interest rate 5.2% compounded quarterly, and that of bank C has an annual interest rate of 5.3% com-

pounded annually. Which bank is the best for you?

2. Logistic Growth Model

Local scientists discovered the spread of a certain disease in their community. The initial infection is 35 people, and

the number of infected people after t days is estimated as follows.

P(t) = 3850

1 + 109.0 ⅇ-0.04 t

(2.1) Estimate the number of infected people after 100 days, 200 days and 365 days.

(2.2) How many days later will the infected population reach 1,500 people?

3. Radioactive Decay Model

Americium-241 is a radioactive substance used in common household smoke detectors. The radioactive decay of Americium-241

can be modeled by the following formula, where Q0 is the initial quantity and the time t is measured in years

Q(t) ≈ Q0 ·  1 2  t / 432.2

(3.1) Suppose that you have 10 milligrams of Americium-241. Estimate the remaining quantity of Americium-241

after (a) 20 years; (b) 200 years; (c) 432.2 years; (d) 864.4 years.

(3.2) How many years later will the remaining quantity be 7.0 milligrams?

4. Logarithmic Scaling Model

The Richter-scale measurement of earthquake is defined as follows.

R = log10(I / S) .

Here, S is the intensity of the standard earthquake whose amplitude is 1 micron, or 10-6m.

The 1906 earthquake in San Francisco had an estimated magnitude of 8.3 in Richter scale. In the same year, a

powerful earthquake occurred on the Columbia-Ecuador border that was four times as intense. What was the Richter

scale of the second earthquake?

2 1324-ex-13&14.nb

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