Ch#7 pH levels · Notes 7.1 Characteristics of Exponential Functions.notebook October 20, 2016...

Notes 7.1 Characteristics of Exponential Functions.notebook October 20, 2016

Ch#7Exponential Functions

compound interest

pH levels


Review of Exponents


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


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


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.


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?


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?


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:

Ch#7 pH levels · Notes 7.1 Characteristics of Exponential Functions.notebook October 20, 2016...

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