Exponential Functions

Graphing Exponential Functions

100

Does the function 

  f(x) = -2/9(5/4)^x

represent exponential growth or decay?  

Exponential growth

200

Graph the function:

f(x) = -(4)^x

On paper

300

What is the end behavior of the graph of an exponential decay function?

As x approaches infinity, f(x) approaches 0.

As x approaches negative infinity, f(x) approaches infinity.  

400

Graph y = 4(1/4)^x

On paper.  

500

Look at the base 2 graph.  Write the equation of the function.  

f(x) = (2)^x+3 -5

Transformations of Exponential Functions

100

How is the function y = 2^x transformed to create the graph of y = -2^(x+3) - 4?

Translated left 3 units, reflected over the x-axis, and translated down 4 units.

200

Describe the transformation that occurs to the graph of the parent function f(x)=2^x to produce the graph of g(x)=2^x+5

Up 5 units

300

Describe the transformation applied to f(x)=5^x to get  g(x)=5^(x−3) 

What is the equation of the horizontal asymptote for g(x)  ?

The graph is shifted right 3 units.
The horizontal asymptote is y=0 (a horizontal shift does not change the position of the asymptote).

400

How does the graph of g(x)=3⋅4^x differ from the graph of its parent function f(x)=4^x 

What is the new y-intercept?

The graph of g(x) is a vertical stretch by a factor of 3.

The y-intercept of the parent function, which is 

(0,1), changes to (0,3) in the new function.

500

Write the equation for an exponential function with a base of 2 that has been shifted left 4 units and shifted down 1 unit.

The equation is y=2^(x+4)−1

Logarithms

100

Write this exponential equation in logarithmic form:   2⁶=64

log₂64=6

200

Evaluate the expression without using a calculator:

log10000

4

300

Write this logarithmic equation in exponential form:

log₃81=4

3⁴=81

400

Evaluate:   log₄(1/64) without using a calculator.  

-3

500

Use the change of base formula to evaluate:

log₅125

Show your work.  

3

log 125/log5

e

100

Write this exponential equation in logarithmic form:

e²=7.389  

ln(7.389)=2

200

Write this logarithmic equation in exponential form:
ln⁡(x)=3

e³=x

300

A bacteria population grows continuously at a rate modeled by   P=500e^0.2t where t is in hours.
Guess and check the time to find how long it takes the population to double.  Round your answer to the nearest hundredth.  

What is about 3.47 hours?

400

What is the difference between the common log and the natural log?  How are they both written?  

Common log is base 10   Ex.  logx

Natural log is base e      Ex.  lnx

500

Evaluate the expression:
ln⁡(e)   No calculator.

What is 1? 

Exponential Growth & Decay

100

Write a simplified exponential function for the scenario: an investment of $20,000 earns 2.5% interest per year

y = 20000(1.025)^x

200

What is the difference between the exponential growth formula and the exponential decay formula?

Growth is addition and decay is subtraction.

300

Kayden's antique car is worth $12,000.  It appreciates in value by 11% each year.  Write the exponential function for this scenario.

y = 12000 (1 + .11)^x or y = 1200(1.11)^x

400

Harold's credit card has 14% annual interest.  All credit card interest is compounded continuously.  His starting balance is $3000.  How much will he owe in 3 years if he makes no other payments or charges to the card? (Harold is making a very bad financial choice.)

$4,565.88

500

A clogged pipe is slowly clearing as the amount of sludge decays exponentially.  The sludge has a half-life of 5 hours and starts with 100 grams.  Write the equation and find how much remains after 15 hours.

What is A=100(1-0.5)^t/5

12.5 grams of sludge remain after 15 hours.