MATH233 Unit 4: Logarithmic Functions

Discussion Board Assignment: Version 2A
Note:All work must be shown and
explained to receive full credit.
The equation to simulate the time that it will take for an investment
to grow based on the interest rate,
compounded monthly, is as follows:
????(????) =
???? > 0
ln(????)
12 ln(1+0.0833????)
whereTis the time in years,ris the interest rate (in decimal form), andkrepresents the growth of the
investment.
1. Choose a value forkfrom the table based on
the first letter of your last name for the investment
that you want to simulate, and set up your equation forT(r).Choose a value ofkthat is different
from your classmates’ values ofk.
First letter of your last name Values fork
Interpretation
A–F
1.10–1.90
Investment will grow 1.10 to 1.90 times
G–L
2.10–2.90
Investment will grow 2.10 to 2.90 times
M–R
3.10–3.90
Investment will grow 3.10 to 3.90 times
S–Z
4.10–4.90
Investment will grow 4.10 to 4.90 times
2. Find the derivative ofT(r)with respect tor,the rate of change in time with respect to the interest
rate using the quotient rule. (Note that ln(k) is a constant.)
3. Choose 5 interest rates between 2% and 20%. Complete the following
table by calculating the
values ofT(r)andT’(r),correctly rounded to two
decimal places. (Note that the rates do not
necessarily have to be whole numbers. Examples such as 5.5% or 9.85%
are acceptable.)
T(r)
T’(r)
Interest Rates,rPLEASE VIEW ATTACHMENT BELOW WHICH CONTAINS ALL QUESTIONS