A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN: 9780134753119
Author: Sheldon Ross
Publisher: PEARSON
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Question
Solution:
If an amount doubles, the rate of increase is 100%
y = a (1 + r)'
y = 1 (1 + 1)*
y = 28
y = 256
Therefore, there are 256 bacteria after 8 minutes.
Exercise
Solve the following problems on exponential growth.
1. In 2002 the population of school children in a city was 90,000. This population
increases at a rate of 2% each year. What will be the population of school children
in year 2010?
2. Janine owns a chain of fast food restaurants that operated 200 stores in 1999. If
the rate of increase is 8% annually, how many stores does the restaurant operate
in 2007?
3. The number of insects in a colony doubles every month. At present there are
25 insects in the colony, about how many insects will there be in the colony
after three months?
GENERAL MATHEMATICS
Week 7 – Day 2
To solve word problems involving exponential functions, equations
and inequalities
Objective
Concept Notes
Any quantity that decays by a fixed percent at regular intervals is said to possess
exponential decay. The pattern can be represented by the function
y = a (1 - r)t
where:
a= initial amount before measuring decay
r = decay
t = number of time intervals that have passed
Example 1:
A cellphone worth P12, 000 was bought three years ago. If it depreciates 5% per
annum, how much does it cost now?
Given:
a = 12,000
r = 5% or 0.05
t = 3 years
Solution:
у 3а (1-г)"
y = P12,000( 1- 0.05)3
у 3D Р 10, 288.50
After 3 years the cost of the cellphone will be P 10, 288.50.
AI TRIPLEarAtM E:RAcay by half-life
Half-life is the amount of time it takes for half of the amount of substance to
Shot by d decay. Scientists and environmentalists worry about such substances beruze these 6 14:15
hazardous material continue to be dangerous for many years after their disposal.
A radioactive element has a half-life of two weeks. How much of 1000-gram
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Transcribed Image Text:Solution: If an amount doubles, the rate of increase is 100% y = a (1 + r)' y = 1 (1 + 1)* y = 28 y = 256 Therefore, there are 256 bacteria after 8 minutes. Exercise Solve the following problems on exponential growth. 1. In 2002 the population of school children in a city was 90,000. This population increases at a rate of 2% each year. What will be the population of school children in year 2010? 2. Janine owns a chain of fast food restaurants that operated 200 stores in 1999. If the rate of increase is 8% annually, how many stores does the restaurant operate in 2007? 3. The number of insects in a colony doubles every month. At present there are 25 insects in the colony, about how many insects will there be in the colony after three months? GENERAL MATHEMATICS Week 7 – Day 2 To solve word problems involving exponential functions, equations and inequalities Objective Concept Notes Any quantity that decays by a fixed percent at regular intervals is said to possess exponential decay. The pattern can be represented by the function y = a (1 - r)t where: a= initial amount before measuring decay r = decay t = number of time intervals that have passed Example 1: A cellphone worth P12, 000 was bought three years ago. If it depreciates 5% per annum, how much does it cost now? Given: a = 12,000 r = 5% or 0.05 t = 3 years Solution: у 3а (1-г)" y = P12,000( 1- 0.05)3 у 3D Р 10, 288.50 After 3 years the cost of the cellphone will be P 10, 288.50. AI TRIPLEarAtM E:RAcay by half-life Half-life is the amount of time it takes for half of the amount of substance to Shot by d decay. Scientists and environmentalists worry about such substances beruze these 6 14:15 hazardous material continue to be dangerous for many years after their disposal. A radioactive element has a half-life of two weeks. How much of 1000-gram
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