# hello! need alittle (read: a lot) of help

#### Dr.Peterson

##### Elite Member
OK, what help do you need?

We can't start helping until we know what you've tried and where you're stuck.

#### enuff4u2nv1

##### New member
I was trying to plug in the numbers to the equation given but the denominator in the exponent is a decimal. So I really dont even know where to start

#### tkhunny

##### Moderator
Staff member
I was trying to plug in the numbers to the equation given but the denominator in the exponent is a decimal. So I really dont even know where to start
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?

#### Dr.Peterson

##### Elite Member
I was trying to plug in the numbers to the equation given but the denominator in the exponent is a decimal. So I really dont even know where to start
You should have shown what you did, so we can see where you are stuck. What you presumably did is the way to start!

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.

#### Subhotosh Khan

##### Super Moderator
Staff member
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.

#### HallsofIvy

##### Elite Member
Are you saying that you don't know how to calculate something like $$\displaystyle 3.7^{0.3525}$$?

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". That is "$$\displaystyle 3.7^{0.3525}$$".

#### enuff4u2nv1

##### New member

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.

unsure of what to do next

#### Jomo

##### Elite Member
You use your formula that has the value for k in it, plug in 2 for t and evaluate. This will give you A(2)

#### Jomo

##### Elite Member
I was trying to plug in the numbers to the equation given but the denominator in the exponent is a decimal. So I really dont even know where to start
Simply multiply the numerator and denominator of the exponent by 10 and wave goodbye to the decimal in the denominator.

#### Dr.Peterson

##### Elite Member
unsure of what to do next
Now 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 "$$\displaystyle 57 \times 0.5\; x^y\; (3\div 5.7)$$".

#### enuff4u2nv1

##### New member
Now 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 "$$\displaystyle 57 \times 0.5\; x^y\; (3\div 5.7)$$".
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.

#### HallsofIvy

##### Elite Member
Yes, Dr. Peterson's "3" should be a "2". Again how you do that depends on what calculator you are using! The calculator that comes with Windows has a "$$\displaystyle x^y$$". With that you would do Dr. Peterson's "57×0.5$$\displaystyle x^y$$(3÷5.7)" where "$$\displaystyle x^y$$" means "press the $$\displaystyle x^y$$ key". Note the parentheses around "3÷5.7". That tells the calculator to do that and then take 0.5 to that power. You can also do that separately, 3÷5.7= 0.71428571428571428571428571428571, use the "M+" key to save it to memory (Perhaps using the "MC" button to clear memory first), then do $$\displaystyle 3\(\displaystyle x^y$$ "MR" (memory recall) to get that number).\)

#### JeffM

##### Elite Member
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.
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))

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.

#### Dr.Peterson

##### Elite Member
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.
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.

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.

#### enuff4u2nv1

##### New member
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.

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.

#### enuff4u2nv1

##### New member
that is the assignment
I have a scientific calculator on my laptop
Calculator 10.1805.1201.0

#### Dr.Peterson

##### Elite Member
I would say that "show all work" means to show the equation you write and the main steps to solve it, including the expression you evaluate to get the final answer. You wouldn't need to show each individual operation you carry out.

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 xy (2 ÷ 5.7)" .

#### enuff4u2nv1

##### New member
I would say that "show all work" means to show the equation you write and the main steps to solve it, including the expression you evaluate to get the final answer. You wouldn't need to show each individual operation you carry out.

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 xy (2 ÷ 5.7)" .
Thank you Dr. Peterson
greatly appreciated