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Suppose that the percent p (as a decimal) of people who could correctly identify two of eight defendants in a drug case t days after their trial began is given by:

p(t) = t^2+ 8.1t+ 0.06

a. Find the number of days before the percent is maximized.
b. Find the maximum percent.

Respuesta :

Answer: a) 4 days, b) Maximized percent = 16.46.

Step-by-step explanation:

Since we have given that

[tex]p(t)=-t^2+8.1t+0.06[/tex]

We need to find the maximum percent and number of days before the percent is maximized.

So, first we derivative the above p(t), we get that

[tex]p'(t)=-2t+8.1[/tex]

Now, we will find the critical points :

[tex]p'(t)=0\\\\-2t+8.1=0\\\\-2t=-8.1\\\\t=\dfrac{-8.1}{-2}\\\\t=4.05[/tex]

So, we will check at t = -4.05, whether it gives maximum percent or not.

So, it becomes,

[tex]p''(t)=-2<0[/tex]

So, a) there would be 4 days before the percent is maximized.

b) maximum percent would be

[tex]p(4)=-(4)^2+8.1(4)+0.06=16.46[/tex]

Hence, a) 4 days, b) Maximized percent = 16.46.

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