Homework Help

What is the answer and how do you solve for question 5.b?...

user profile pic

lkballer24 | Student, Grade 11 | (Level 1) Valedictorian

Posted April 22, 2013 at 7:06 PM via web

dislike 1 like

What is the answer and how do you solve for question 5.b?


2 Answers | Add Yours

user profile pic

rcmath | High School Teacher | (Level 1) Associate Educator

Posted April 22, 2013 at 8:17 PM (Answer #1)

dislike 1 like

The function is `f(x)=0.25*4^x-2`
by looking at the answer for the first part of the question (please see the reference link below), we notice that as the values are getting closer to zero the slope is decreasing. 
So we will have to asuume that the slope will eventually decrease to zero. So your tangant will be a horizontal line.
That can be proved by looking at the limit as x approches zero of 
`(0.25*4^x-2-(0.25-2))/(x-0)=(.25*4^x-2-0.25+2)/x=(.25*4^x-0.25)/x` , the limit of such a function is 0.






user profile pic

oldnick | (Level 1) Valedictorian

Posted April 23, 2013 at 12:00 AM (Answer #2)

dislike 1 like

`f(x)=1/4 4^x -2=4^(x-1)-2` `=2^(2(x-1))-2`


`f'(x)=2^(2x-1) log2` 

So  `m= f'(0)= 1/2log2`  and  `f(0)= -7/4`

tangent straigth line equation is


`y-7/4=1/2 x log2 `


Red line: function

Blue line: tangent straight line

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes