# Need help with P(t) = [ 73t^(1/3) - 28t^(2/3) ] / t

#### stormer

##### New member
Can someone help me with this problem?

. . .P(t) = [ 73t^(1/3) - 28t^(2/3) ] / t

Should the top be written as a rational equation? 73 t cubed and 28t cubed??

#### stapel

##### Super Moderator
Staff member
Why would the numerator (an expression) be converted to another type of object (an equation)? Why would the cube roots turn into cubes?

What are the instructions for this? What are you trying to do? Please be specific. Thank you.

Eliz.

#### stormer

##### New member

This is a word problem that we are doing for extra credit. It is as follows:

According to the American Medical Association, the percentage of potential employees testing positive for ill eagle drugs on the decline.
The Function (P(t) = Insert equation here) models the percentage P(t), of people applying for jobs who test positive (t) years after 1985.
What percentage of people applying for jobs tested positive for illegal drugs in 1993?

Any help would be greatly appreciated

#### soroban

##### Elite Member
Hello, stormer!

According to the American Medical Association,
the percentage of potential employees testing positive for illegall drugs on the decline.

The function: $$\displaystyle \L P(t)\:=\:\frac{73t^{\frac{1}{3}}\,-\,28t^{\frac{2}{3}}}{t}\,$$ models the percentage $$\displaystyle P(t)$$
$$\displaystyle \;\;$$of people applying for jobs who test positive $$\displaystyle t$$ years after 1985.

What percentage of people applying for jobs tested positive for illegal drugs in 1993?

Your questions are scary . . .

Don't say "equation" unless you mean it.

We are given cube roots . . . you're asking about cubes?

$$\displaystyle 1993$$ means $$\displaystyle t\,=\,8$$ . . . Plug it in !

#### Denis

##### Senior Member
P(t) = [ 73t^(1/3) - 28t^(2/3) ] / t
Why are you complicating it?

t = 1993 - 1985 = 8

P(t) = [ 73 * 8^(1/3) - 28 * 8^(2/3)] / 8

8^(1/3) = 2 : 2*2*2 = 8
8^(2/3) = (8^2)^(1/3) = 64^(1/3) = 4 : 4*4*4 = 64

Finish it.