Derivative problem: changing effectiveness of medication

[AGlas9837]

I need help with the following word problem:

The effectiveness "E" (on a scale from 0 to 1) of a pain-killing drug "t" hours after entering the bloodstream is given by:

E = 1/27(9t + 3t^2 - t^3); t is between 0 and 4.5

The derived (and reduced?) equation, according to my solutions manual, is 1/9(3 + 2t - t^2).

I understand what to do with the x/y values once I've obtained them but am not getting the same values as my book gives. For example, for E of 1, I get 4/9 and for E of 2 I get 3/9. So I'm trying to understand how you get the following y values:

11/27 for E of 1,
23/27 for E of 2,
1 for E of 3
20/27 for E of 4

Thanks in advance!!

 

[Deleted member 4993]

Re: Derivative problem

The effectiveness "E" (on a scale from 0 to 1) of a pain-killing drug "t" hours after entering the bloodstream is given by:

E = 1/27(9t + 3t^2 - t^3); t is between 0 and 4.5

The derived (and reduced?) equation, according to my solutions manual, is 1/9(3 + 2t - t^2).

I understand what to do with the x/y values once I've obtained them but am not getting the same values as my book gives. For example, for E of 1, I get 4/9 and for E of 2 I get 3/9.

How did you get these values - please show work

 

[AGlas9837]

I've actually since figured this out...thanks.