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**Exponential Functions**

John Napier

Born: 1550 Died: 4th April 1617, at the age 67

Joost Burgi

Born: February 28, 1552

Died: January 31, 1632

Leonard Euler

Born: Born: 15 April, 1707 Died: 18 September 1783

𝑒^(ln(𝑥))=𝑥 if 𝑥>0

Discovered logarithm

Invented: Logarithm, Exponential Notation

What's an Exponential Function?

Basic exponential function equation

Positive Real Numbers:

(0,+∞)

Y -Intercept

Horizontal Asymptote

**Example Problems**

**Exponential Models**

P

o

is the initial size of the population at time zero

P(

t

) is the population size after time

t

**The Spread of Virus**

**Ebola**

Growth Factor k>0

Decay Factor k<0

On March 1, 2014 it was reported that 58 people were either infected with Ebola or had died from it since the first believed case on December 6, 2013.

How many people were

infected

after the first known case?

P(t)=58e^0.0216(252+365) = 35,592,411

1 Year Later

What will the World Population be in 2016?

Example Problem

P(t)=Poe^kt

P(6)=7.0e^(0.01042(6)) = 7.45 Billion People

Po= 7 Billion People

t= 2016

k= 1.042%

Using Exponential Notation, how many people were infected by November 7, 2014?

The

principle amount (Po)

= 58

The

growth rate (k)

= 2.16%

The

time

(t) = 252 days

P(t)=58e^0.0216(252) = 13,408

Napier Bone

constant (

base

)

variable(

exponent

)

The problem says we have to multiply x number of two's together to get four. Well, everyone knows that 2*2=4, so the answer is two:

4= 2^2

x=2

If 865 days passed from the date of the first infection, how many people will either be infected and/or have died as a result of Ebola at a growth rate of 2.16 percent?

P(t)=58e^0.0216(t) = ?

P(t)=58e^0.0216(

865

) =

7,547,204,076

*Est. world population in 2016 = 7.45 billion

𝑥^𝑚 𝑥^𝑛=𝑥^(𝑚+𝑛)

Characteristics

July 12, 2016

e= 2.718281828..

To Conclude..

Class Activity

Out the twenty-five students in the classroom, initially, eight students will receive a candy gummy worm, which represent the Ebola virus itself.

Every 7 minutes 4 students are infected. After 35 minutes the entire class will be infected with the Ebola virus

Po=25 Students

P=8 Students

k=6.4% Or 0.64

T=7 Minutes (420 sec.)

P(420)= 8e^0.64(420) =3.7

Four students after seven minutes are infected with the Ebola virus.

**Gabriela Oyola**

Ivetteliz Torres

Keishawn Dew

Nehemie Verdier

Ivetteliz Torres

Keishawn Dew

Nehemie Verdier

Solve for x: 4=2^x