Exponential Functions and Equations

7.1 Exponential Functions and Equations

​Common Bases: Rewrite the expression (powers)

​1²=

​2²⁼

​3²⁼

​4²⁼

​5²⁼

​6²⁼

​7²⁼

​8²⁼

​9²=

​1³=

​2³⁼

​3³⁼

​4³⁼

​5³⁼

​6³⁼

​7³⁼

​8³⁼

​9³=

​1⁴=

​2⁴⁼

​3⁴⁼

​4⁴⁼

​5⁴⁼

​6⁴⁼

​7⁴⁼

​8⁴⁼

​9⁴=

Multiple Choice

To Solve an exponential equation you must...

• Rewrite the expressions using the common base

• Divide both sides

• Cancel the even numbers

• Cry

Multiple Choice

Solve

$$27^x=81.$$  

• $$x=\frac{4}{3}$$  

• $$x=\frac{3}{4}$$  

• $$x=-\frac{4}{3}$$  

• $$x=-\frac{3}{4}$$  

Multiple Choice

Solve

$$8^x=4.$$  

• $$x=-\frac{2}{3}$$  

• $$x=\frac{2}{3}$$  

• $$x=\frac{3}{2}$$  

• $$x=\frac{1}{2}$$  

Multiple Choice

Solve

$$4^x=32.$$  

• $$x=\frac{3}{4}$$  

• $$x=\frac{2}{5}$$  

• $$x=\frac{5}{2}$$  

• $$x=\frac{1}{4}$$  

Multiple Choice

Solve

$$3^x=\frac{1}{27}.$$  

• $$x=-2$$  

• $$x=3$$  

• $$x=-3$$  

• $$x=9$$  

Multiple Choice

Solve

$$3^{\left(x+1\right)}=27.$$  

• $$x=2$$  

• $$x=4$$  

• $$x=-4$$  

• $$x=-2$$  

Multiple Choice

Find the solution for

$$5^{\left(x+7\right)}=25^x.$$  

• $$x=2$$  

• $$x=-2$$  

• $$x=-7$$  

• $$x=7$$  

Exponential Functions have a variable in the exponent

Multiple Choice

Which of the following is an exponential function?

• y = x²

• f(x) = 3x³

• y = x³

• f(x) = 3^x

Exponential

Growth vs. Decay

If b > 1 : Growth

If 0<b<1 (fraction): Decay

Both Graphs have a

Horizontal Asymptote

(graph never touches

the X-axis)

b^x cannot equal 0

Multiple Choice

What does the graph represent?

• Exponential Growth

• Exponential Decay

Multiple Choice

What does this graph represent?

• Exponential Growth

• Exponential Decay

Multiple Choice

Which does y= 2(.5)^x represent?

• Exponential Growth

• Exponential Decay

Multiple Choice

Which does y=.5(2)^x represent?

• Exponential Growth

• Exponential Decay

Multiple Choice

What is the initial value of the situation represented by f(x)=0.05(2)^x?

• 0.05

• 2

• 0.1

• 1

Multiple Choice

This is the horizontal line which the values of the function cannot fall below :

• Asymptote

• Growth Factor

• Axis of symmetry

• Curve

Multiple Choice

Cells dying off would be represented by which of the following?

• Exponential Growth

• Exponential Decay

Multiple Choice

Bacteria growing can be represented by which of the following?

• Exponential Growth

• Exponential Decay

Multiple Choice

Is the following function and example of decay or growth?

f(x)=2(0.85)^x

• Exponential Decay

• Exponential Growth

Fill in the Blanks

Jacob borrows $500 from Abraham and agrees to have the loan compounded annually for 5 years with an interest rate of 2.5%. How much will the total amount be that Jacob owes?

Fill in the Blanks

Hei-Hei has $1500 in a retirement account earning 5% interest compounded continuously. After 5 years how much does Hei-Hei have in the account?