1. ## exponential growth test

tomorrow I'll be taking a test on exponential growth, things like the growth rates of bacteria. the basic formula that we're using is Y=a(b)^x/c. I am fine with this on till we start adding negatives to the mix. for example

Y=6(2)^-4/6

I understand that the base(6) is going to be multiplied by the factor(2) and although i partially understand how to punch a fraction for an exponent into the calculator, i don't understand exactly how it works, and when the fraction becomes a negative, my calculator answer dos not come out correct ether.

2. Originally Posted by counting monkeys
tomorrow I'll be taking a test on exponential growth, things like the growth rates of bacteria. the basic formula that we're using is Y=a(b)^x/c. I am fine with this on till we start adding negatives to the mix. for example

Y=6(2)^-4/6

I understand that the base(6) is going to be multiplied by the factor(2) and although i partially understand how to punch a fraction for an exponent into the calculator, i don't understand exactly how it works, and when the fraction becomes a negative, my calculator answer dos not come out correct ether.
What model do you have?

$\displaystyle Y = 6 \times 2^{-\frac{4}{6}}$

First you can cancel $\displaystyle \frac{4}{6} = \frac{2}{3}$

It means you raise the 2 to the $\displaystyle -\frac{2}{3}$ which means

$\displaystyle \frac{1}{2^{-\frac{2}{3}}}$

3. i don't know what you mean by model but the thing i really don't understand is what happens when the exponent is a fraction and is negative

4. Originally Posted by counting monkeys
i don't know what you mean by model but the thing i really don't understand is what happens when the exponent is a fraction and is negative
$\displaystyle x^{-\frac{a}{b}}= \frac{1}{x^{\frac{a}{b}}} = \frac{1}{\sqrt[b]{x^a}}$, that's what happens

5. i don't mean to sound ungrateful for you help, but is this the kind of forum some one should be on if they don't understand the math alone?

6. Originally Posted by counting monkeys
tomorrow I'll be taking a test on exponential growth, things like the growth rates of bacteria. the basic formula that we're using is Y=a(b)^x/c. I am fine with this on till we start adding negatives to the mix. for example

Y=6(2)^-4/6

I understand that the base(6) is going to be multiplied by the factor(2) and although i partially understand how to punch a fraction for an exponent into the calculator, i don't understand exactly how it works, and when the fraction becomes a negative, my calculator answer dos not come out correct ether.
I don't see what the problem is in typing 2^(-4/6) into your calculator. Are you using brackets (look where mine are)? If you type 2^-4/6 your calculator will think you mean something different to 2^(-4/6). Are you using the negative button on your calculator when you type this expression ....? If you're using the minus button your calculator won't like it.

Also note that 2^(-4/6) = 1/2^(4/6) using a well known index law.

It is impossible to know what your real problem is but it probably boils down to incorrect data entry on your calculator. Run it past your teacher.

7. thanks, the bracket thing really makes seance, now i just have to learn the why behind the how