#### enuff4u2nv1

##### New member

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- Thread starter enuff4u2nv1
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Please read this, and follow it:

Welcome to our tutoring boards! :) This page summarizes some main points from our posting guidelines. As our name implies, we provide math help (primarily to students with homework). We do not generally post immediate answers or step-by-step solutions. We prefer to help by having a...

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We can't start

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Why does it matter if it's "a decimal"? Are you calculating it with paper and pencil? Why not just use the exponent button on your calculator?

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You should have shown what you did, so we can see where you are stuck. What you presumably did

My guess is that you are thinking of the exponent merely as a fraction, and forgetting that that is the same thing as a division.

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First thing you need to do is to

Find the value of C from "the amount of caffeine in the entire container" - what did you get?

Second, calculate the value "k" - knowing the half-life.

Continue and post your work.......

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When I was in school, in yearS "B. C" (before calculators), we used "logarithms". If \(\displaystyle A= 3.7^{0.3525}\) then \(\displaystyle log(A)= log(3.7^{0.3525})= 0.3525 log(3.7)\). So look up the logarithm of 3.7 (in a "table of logarithms), multiply by 0.3525, then look up the anti-logarithm in that same table.

But now, every one has a calculator or computer (I haven't owned a calculator in many years, I use the calculator that comes with "Windows"). The calculator that comes with "Windows" has a "\(\displaystyle x^y\)" key that does that- enter "3.7", press the "\(\displaystyle x^y\)" key, enter "0.3525", then press "=" and get "1.5859559030154998131349031116977".

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Simply multiply the numerator and denominator of the exponent by 10 and wave goodbye to the decimal in the denominator.

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Now you just type that expression, \(\displaystyle 57(0.5)^{2/5.7}\), into your calculator. What kind of calculator do you have?unsure of what to do next

Typically, you'll type in something like "57 * 0.5 ^ ( 3 / 5.7)" or "\(\displaystyle 57 \times 0.5\; x^y\; (3\div 5.7)\)".

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scientificNow you just type that expression, \(\displaystyle 57(0.5)^{2/5.7}\), into your calculator. What kind of calculator do you have?

Typically, you'll type in something like "57 * 0.5 ^ ( 3 / 5.7)" or "\(\displaystyle 57 \times 0.5\; x^y\; (3\div 5.7)\)".

should that 3 be a 2?

in regards to the actual steps to solve, would I do the exponent 1st? (.5)^(2/5.7)

I have to show this step by step. I can't just provide the answer. That is why I'm trying to get an understanding for how to actually work the equation.

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Well a lot depends on your calculator. On my calculator, I would probably clear memory, calculate 2/5.7 and store that in memory. Then I would enter 0.5 and then x^y, hit recall from memory, and multiply the result by 57. If your calculator has parentheses, you could also use them to organize the order of operations. Hit 57, multiply, ( 0.5, x^y, ( 2, divide, 5.7))scientific

should that 3 be a 2?

in regards to the actual steps to solve, would I do the exponent 1st? (.5)^(2/5.7)

I have to show this step by step. I can't just provide the answer. That is why I'm trying to get an understanding for how to actually work the equation.

I would show it like this

\(\displaystyle 57 * 0.5^{2/5.7} \approx 44.6941\)

It is really sloppy to round intermediate results.

If you think that is required (UGH!) then you could show

\(\displaystyle \dfrac{2}{5.7} \approx 0.35\\

0.5^{0.35} \approx 0.78\\

57 * 0.78 = 44.46.\)

As you can see, rounding intermediate results gives you a poorer approximation.

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There are quite different kinds of scientific calculators; you may need to either tell us the make and model, or at least describe it fully. For example, some display only a number, while others show what you have entered, which may be on a line or formatted as in a book. Each of these requires different keystroke sequences.scientific

in regards to the actual steps to solve, would I do the exponent 1st? (.5)^(2/5.7)

I have to show this step by step. I can't just provide the answer. That is why I'm trying to get an understanding for how to actually work the equation.

But for any kind, you need to use whatever mechanism it provides to evaluate the exponent before applying it.

Also, do you have an example of how you are expected to show steps? It may require less than you think.

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But for any kind, you need to use whatever mechanism it provides to evaluate the exponent before applying it.

Also, do you have an example of how you are expected to show steps? It may require less than you think.

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I have a scientific calculator on my laptop

Calculator 10.1805.1201.0

© 2018 Microsoft. All rights reserved.

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The Windows calculator, in Scientific mode, is the type where you generally enter a number followed by the operation you need to do (e.g. press the square root button after entering the radicand); but for this expression, you will enter it more or less as written, apart from needing parentheses around the exponent. As I said before, "57 × 0.5 x

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Thank you Dr. Peterson

The Windows calculator, in Scientific mode, is the type where you generally enter a number followed by the operation you need to do (e.g. press the square root button after entering the radicand); but for this expression, you will enter it more or less as written, apart from needing parentheses around the exponent. As I said before, "57 × 0.5 x^{y}(2 ÷ 5.7)" .

greatly appreciated