Exponential Functions + Basic Log

The graph of f(x) = Ca^x contains the point (0,_)(1,_)(-1,_).

(0,C) (1,Ca) (-1, C/a)

What is the domain of Ca^x?

All real numbers

What are the aspects of exponential functions vs linear functions?

Exponential qualities: →F(x) = a^x →Slope is changing Linear qualities: →Slope is constant →If graphed it, it makes a line →y = mx+b

How do you solve for x in the equation: ³√3^X = ³√27 (How do you solve exponential equations for x)

First, you make the base numbers equal to one another by rewriting them as exponents when needed: ³√3^X = ³√3^3 Then, you solve for x by setting each exponent equal to one another, which in this case shows you directly that x=3.

If a>1, the function is __________. If a>1, it is called the ________ factor.

Increasing growth

Explain why any exponential function f(x) cannot equal zero.

It can never equal zero because there is no exponent that makes any real number equal to zero.

How can you tell in table format if the function is exponential, linear or neither?

Linear growth: added by the same number consistently Exponential growth: multiplied by the same number consistently Neither: Doesn't follow either ↑

What is the equation to a logarithmic function?

Log(a)X=Y a = Base number Y = exponent X = a^y

What is the equation for exponential growth over time?

P(t)=P₀(1+r)^t

What does P₀, r, t stand for in exponential growth equation?

P₀ = Principal r= rate t= time

in f(x) = Ca^x, C is called what?

The initial value.

What intercepts are located on the graph of f(x) = Ca^x?

There are no x-intercepts, y-intercept is (o,c)

What is the rule of exponents when you turn a base number X, like in X^a into an exponent Y^b?

You multiply the b by the base exponent a: X^a = Y^b(a)

If 0<a<1, the function is __________. If 0<a<1, it is called the ________ factor.

decreasing decay

What variable stands for 'continuous growth'?

e

What is the basic exponential function equation?

f(x) = Ca^x

The figure f(x) = Ca^x (is/isn't) smooth and continuous with no corners or gaps

it IS smooth and continuous.

What is the horizontal asymptote in f(x) = Ca^x?

the X-axis.

What is official check-answer format?

x=2 4 ?= 2^x 4=2^2 4 = 4 √ The solution set is {2}

What is the equation for continuous growth?

y = (1+1/n)ⁿ

What is the range of Ca^x

{y|y>0}