Algebra House
  • Ask a Question
    • Answered Questions
  • Examples
  • State Test Practice
    • Algebra 1 State Test Practice
    • Geometry State Test Practice
  • ACT and SAT
  • Calculators
    • Problem Solver
    • Graphing Calculator
    • 3D Graphing Calculator
  • Contact
    • Contact Algebra House
    • Leave a Tip


​
​ALGEBRA 1 STATE TEST PRACTICE

Interpret the average rate of change of a function

2/3/2015

0 Comments

 
At the beginning of an experiment, the number of bacteria in a colony was counted at time t = 0.  The number of bacteria in the colony t minutes after the initial count is modeled by the function b(t) = 4(2)^t.  Which value and unit represent the average rate of change in the number of bacteria for the first 5 minutes of the experiment?   Select all that apply.
A.)  24.0                      E.)  bacteria
B.)  24.8                      F.)  minutes
C.)  25.4                      G.)  bacteria per minute
D.)  25.6                      H.)  minutes per bacteria

The input into the function is t
The output of the function is b(t)


Think of t as the x-value {input}
Think of b(t) as the y-value {output}


Rate of change is slope.

If t = 0
b(t) = 4(2)^0   {substituted 1, in for t, into b(t) = 4(2)^t}
      = 4(1)   {evaluated exponent}
      = 4   {multiplied}

(0,4) is one set of coordinates


If t = 5
b(t) = 4(2)^5   {substituted 5, in for t, into b(t) = 4(2)^t}
       = 4(32)   {evaluated exponent}
       = 128   {multiplied}
(5,128) is another set of coordinates

y2 - y1
--------- = slope
x2 - x1


(0,4) and (5,128)   {the two points}

128 - 4
----------- = slope   {substituted coordinates into slope formula}
  5 - 0

124
----- = slope   {subtracted in numerator and denominator}
  5

Rate of change is  24.8 bacteria per minute

B.)  and  G.)

Ask Algebra House


0 Comments

Your comment will be posted after it is approved.


Leave a Reply.


    Ask a Question
    Latest Videos
    Picture


    Algebra 1 State Test Practice Archives

    August 2023
    November 2021
    May 2021
    April 2021
    March 2021
    February 2021
    January 2021
    December 2020
    January 2020
    December 2019
    November 2019
    October 2019
    September 2019
    August 2019
    April 2019
    January 2019
    December 2018
    September 2018
    February 2018
    January 2018
    December 2017
    November 2017
    September 2017
    April 2017
    March 2017
    February 2017
    December 2016
    October 2016
    September 2016
    January 2016
    December 2015
    November 2015
    October 2015
    September 2015
    July 2015
    April 2015
    March 2015
    February 2015
    January 2015
    December 2014





In case you missed it:
Go Home
​​Ask a Question
Answered Questions
Algebra Examples
State Test Practice

ACT and SAT Practice
​
Notes Archive​
Leave a Tip
​​Problem Solver
Graphing Calculator
3D Graphing Calculator
​Privacy Policy
​
Cookie Policy
  • Ask a Question
    • Answered Questions
  • Examples
  • State Test Practice
    • Algebra 1 State Test Practice
    • Geometry State Test Practice
  • ACT and SAT
  • Calculators
    • Problem Solver
    • Graphing Calculator
    • 3D Graphing Calculator
  • Contact
    • Contact Algebra House
    • Leave a Tip