Download Lesson Two Exponential and Logarithmic Word

Continuous and
Discrete Growth
and Decay
Questions
If $2000 is deposited into an account that pays 7% annual interest
compounded monthly, how much is present in the account after 15 years.
Answer:
$5697.89
The half-life of radium is about 1600 years. If 1 kilogram is present now,
how much will be present after 800 years?
Answer: 707 grams
The number of trees in a forest increases continuously at a rate of
3.5% every year. If the forest currently has 3,350 trees in it, how
many trees were in the forest 4 years and 3 months ago?
Answer:
approximately 2887 trees
The price of a computer decreases exponentially at a rate of .98%
every year, compounded quarterly. If the computer currently costs
$3400, how much will it cost after 10 years?
Answer:
$3082.24
If $3000 is invested in a bank account that pays 5% annual interest
compounded monthly. How many years will it take, to the nearest
month, before you have $5000?
Solution: 10 years and 3 months
The number of bacteria in a colony increases at a continuous rate of
1.5% every hour. If the colony began with 100 cells, how many hours,
to the nearest hour, will it take to reach 500 cells?
Solution: 107 hours
The number of bacteria in a culture currently doubles every 5 days. If
the culture has 75 cells, how many days, to the nearest day, before
there is 200 cells in it?
Solution: 7 days
The population of a country increases at a continuous rate of 1.9%
every year. If the country currently has 3.7 million people find the
minimum number of years before there is at least 8.2 million people.
Solution: 42 years
A sum of $100 is invested.
a) If the interest is compounded annually at a rate if 5% per year,
find the total value V of the investment after 20 years.
5
% per
12
month, find the minimum number of months for the value of the
b) If these interest is compounded monthly at a rate of
investment to exceed V.
Answers:
a) $265.33
b) n = 235
N06/HL1/8