Dear friends, Please read our latest blog post for an important announcement about the website. ❤, The Socratic Team

What is an exponential function?

2 Answers
Write your answer here...
Start with a one sentence answer
Then teach the underlying concepts
Don't copy without citing sources
preview
?

Answer

Write a one sentence answer...

Answer:

Explanation

Explain in detail...

Explanation:

I want someone to double check my answer

Describe your changes (optional) 200

1
Jim H Share
Mar 23, 2015

An exponential function is a function of the form #f(x)=a^x# with #a>0# but #a!=1#.

For integer and rational #x#, we give definitions of #a^x# earlier in algebra classes.
For irrational #x# we owe you a definition, but one approach to the definition is to describe #a^x# for irrational #x# as the number thar #a^r# gets closer to as rational #r# get close to #x#. (We owe you a proof that there is a unique such number.)

Examples:

#f(x)=2^x#

#f(x)=5^x#

#f(x)=(2/5)^x#

#f(x)=4^x=(2^2)^x = 2^(2x)#

The last example illustrates why we also consider #f(x)=a^(kx)# for constant #k!=0# to be exponential functions

We can write #f(x)=a^(kx)=(a^k)^x# and .for #a>0# and #k!=0# this #f(x)=b^x# for the "right kind" of #b#. (#b>0#, and #b!=1#)

Was this helpful? Let the contributor know!
1500
Write your answer here...
Start with a one sentence answer
Then teach the underlying concepts
Don't copy without citing sources
preview
?

Answer

Write a one sentence answer...

Answer:

Explanation

Explain in detail...

Explanation:

I want someone to double check my answer

Describe your changes (optional) 200

1
Deevona Share
Mar 23, 2015

The exponential function is used to model a relationship in which a constant change in the independent variable gives the same proportional change in the dependent variable.

www.cliffsnotes.com

The function is often written as exp(x) It is widely used in physics, chemistry, engineering, mathematical biology, economics and mathematics.

Was this helpful? Let the contributor know!
1500