SOLUTION: Hello, can someone please help me with this problem: Rewrite y=5(1/4)^{t/6} in the form y=a(1+r)^t or y=a(1-r)^t. Round the value of r to the nearest ten-thousandth. Then tell wh

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Hello, can someone please help me with this problem: Rewrite y=5(1/4)^{t/6} in the form y=a(1+r)^t or y=a(1-r)^t. Round the value of r to the nearest ten-thousandth. Then tell wh      Log On


   

Question 1155461: Hello, can someone please help me with this problem:
Rewrite y=5(1/4)^{t/6} in the form y=a(1+r)^t or y=a(1-r)^t. Round the value of r to the nearest ten-thousandth. Then tell whether the model represents exponential growth or exponential decay.
I know that it represents exponential decay but I don't understand how to rewrite in that form.
Someone, please help. Thanks
Found 3 solutions by MathLover1, ikleyn, MathTherapy:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
y=5%281%2F4%29%5E%28t%2F6%29 in the form y=a%281%2Br%29%5Et or y=a%281-r%29%5Et.
=> a=5
5%281%2F4%29%5E%28t%2F6%29=5%281%2Br%29%5Et .....simplify
%281%2F4%29%5E%28t%2F6%29=%281%2Br%29%5Et+
%281%2F2%5E2%29%5E%28t%2F6%29=%281%2Br%29%5Et+
%282%5E-2%29%5E%28t%2F6%29=%281%2Br%29%5Et+
matrix%282%2C1%2C+%22%22%2C2%5E%28-2t%2F6%29=%281%2Br%29%5Et%29
matrix%282%2C1%2C+%22%22%2C2%5E%28-t%2F3%29=%281%2Br%29%5Et%29.....take log of both sides
log%282%5E%28-t%2F3%29%29=log%28%281%2Br%29%5Et+%29
%28-t%2F3%29log%282%29=t%2Alog%28%281%2Br%29+%29
%28-t%2F3%29log%282%29%2Ft=log%28%281%2Br%29+%29
-%281%2F3%29log%282%29=log%28%281%2Br%29+%29
log%282%5E%28-1%2F3%29%29=log%28%281%2Br%29%29
matrix%282%2C1%2C+%22%22%2Clog%281%2F2%5E%281%2F3%29%29%29=log%28%281%2Br%29+%29...if log same, we have
1%2Froot%283%2C2%29=1%2Br.....solve for r
r=+1%2Froot%283%2C2%29+-+1

in the form y=a%281%2Br%29%5Et:
y=5%281%2B1%2Froot%283%2C2%29+-+1%29%5Et
y=5%281%2Froot%283%2C2%29+%29%5Et
check if:
5%281%2F4%29%5E%28t%2F6%29=5%281%2Froot%283%2C2%29+%29%5Et+-> true

in the form y=a%281-r%29%5Et:
=> y=5%281-%281%2Froot%283%2C2%29+-+1%29%29%5Et
y=5%281-1%2Froot%283%2C2%29+%2B+1%29%5Et
y=5%282-1%2Froot%283%2C2%29+%29%5Et

check: 5%281%2F4%29%5E%28t%2F6%29%3C%3E5%282-1%2Froot%283%2C2%29+%29%5Et-> not true

so, your answer is: y=5%281%2Froot%283%2C2%29+%29%5Et


Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.

            Hello,   it is very simple to do.
            I will show it to you now. 


y = 5*(1/4)^(t/6).           (1)


According to the properties of exponents


    y = 5*((1/4)^(1/6))^t.   (2)    


Calculate  (1/4)^(1/6).  It is (use your calculator)


    (1/4)^(1/6) = 0.793701 = 1 -r.


Hence,  r = 1 - 0.793701 = 0.206299,  

or, rounding the value of "r" to the nearest ten-thousandth,

    r = 0.20630.


Therefore, your answer is   y = 5*(1-0.20630)^t.


It is  EXACTLY  the form you requested, with the value of r = 0.20630, rounded as it is assigned by the problem.

--------------

I answered your question.   My answer is  EXACTLY  what the problem asks about.

        What @MathLover wrote in her post,  is

           1)   IRRELEVANT,

      and

           2)   GIBBERISH.


For your safety,  simply ignore her post.

She wrote similar   GIBBERISH   yesterday two or more times,  answering other your posts.

You may ignore her writing too,   by the same reasons.


/\/\/\/\/\/\/\/

Dear @MathLover1,

now I really think that the time just came for you to stop your exercises at this forum.



Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Hello, can someone please help me with this problem:
Rewrite y=5(1/4)^{t/6} in the form y=a(1+r)^t or y=a(1-r)^t. Round the value of r to the nearest ten-thousandth. Then tell whether the model represents exponential growth or exponential decay.
I know that it represents exponential decay but I don't understand how to rewrite in that form.
Someone, please help. Thanks 
To add to Tutor @ IKLEYN's observation, why does that woman use the form: matrix%281%2C3%2C+y%2C+%22=%22%2C+a%281+%2B+r%29%5Et%29 when it's clear that it's an EXPONENTIAL decay (the 1%2F4 in 5(1/4) clearly indicates this)? 

In addition, didn't the person who asked for help clearly state that he/she KNOWS that "it represents exponential decay"?

It doesn't even make sense to point out her NUMEROUS ERRORS because it's either she ignores the notes to her, or she's just not

convinced that most of what she does is RUBBISH, and that she's NOT helping the people who need and ask for assistance, at all!