ch#7 ph levels · notes 7.1 characteristics of exponential functions.notebook october 20, 2016...
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Notes 7.1 Characteristics of Exponential Functions.notebook October 20, 2016
Ch#7Exponential Functions
compound interest
pH levels
Notes 7.1 Characteristics of Exponential Functions.notebook October 20, 2016
Review of Exponents
Notes 7.1 Characteristics of Exponential Functions.notebook October 20, 2016
Notes 7.1 Characteristics of Exponential Functions.notebook October 20, 2016
Notes 7.1 Characteristics of Exponential Functions.notebook October 20, 2016
Notes 7.1 Characteristics of Exponential Functions.notebook October 20, 2016
Notes 7.1 Characteristics of Exponential Functions.notebook October 20, 2016
Section 7.1 Characteristics of Exponential Functions
Exponential function is a function of the form where c is a constant, c > 0, and c ≠ 1, and x is a variable.
exponential decayexponential growth
Notes 7.1 Characteristics of Exponential Functions.notebook October 20, 2016
Characteristics of Exponential Functions of the form
where c > 0
increases for c > 1
decreases for 0 < c < 1
neither increases or decreases for c = 1
domain
range
yintercept of 1
no xintercept
horizontal asymptote at y = 0
Notes 7.1 Characteristics of Exponential Functions.notebook October 20, 2016
Applications for Exponential Problems
where P is the population after time has elapsedPo is the original population c is the rate at which it is growing or decreasingt is the elapsed time
Ex(1) Each of the following situations can be modeled using an exponential function. Indicate which situations model exponential growth and which situations model exponential decay. Also, give the value of c.(a) The summertime population of gophers in a field increases by 10 % every year.
(b) The value of a new car decreases at a rate of rate of 15 % per year.
(c) The halflife of Uranium232 is 68.9 years.
(d) A type of bacterium doubles every 45 minutes.
(e) Money invested in a bank earns 2.5 % compounded annually.
Notes 7.1 Characteristics of Exponential Functions.notebook October 20, 2016
Ex(3) The intensity of the light below the surface of a lake is reduced by 4 % for every meter below the surface. What percent of the original intensity remains 10 m below the surface?
Ex(4) John buys a new vehicle for $ 28 000. It depreciates by 15 % each year. What is the vehicle worth in 7 years?
Ex(2) The world's population is growing exponentially. In 1970 it was about 3.6 billion. If the population increased at 2 % per year since then, what will be the population in 2020?
Notes 7.1 Characteristics of Exponential Functions.notebook October 20, 2016
Ex(6) The halflife of a certain isotope is 2 days. How much will be left from a mass of 500 g after
(a) 6 days? (b) 2 weeks?
Ex(5) An initial count of bacteria shows 1000. It triples every 25 hours.
(a) Write an equation to model this situation.
(b) How many bacteria will there be in 4 days?
(c) How many bacteria were there 3 days prior to the initial count?
Notes 7.1 Characteristics of Exponential Functions.notebook October 20, 2016
Pages 342 344# 1 4, 6, 7, 8(a,c), 9(a,d), and 10(a,c,d)
Write theexponentialequation
careful withthis one
Answers #6: