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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.
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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.
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: when it's clear that it's an EXPONENTIAL decay (the 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!