Differential Calulus Absolute Max and Min

label Calculus
account_circle Unassigned
schedule 1 Day
account_balance_wallet $5

A disease arrives, % of infected is max after 8 days.  Evaluate for p.

p(t)=9te^-t/8

t=8

how do I evaluate for p?

Jul 13th, 2014

So you can verify that max is at t=8 by taking the derivative of p(t) and setting it equal to zero (i.e., calculate t-value where p'(t)=0).

p'(t) = 9*e^(-t/8) + (9t)*(-1/8)*(e^(-t/8)) = 9*e^(-t/8)*(1-t/8)

For max, set p'(t) = 0; thus t=8

Now, we just need to plug t=8 into the original equation for p(t);

Thus: p(8) = 9*8*e^(-8/8) = 9*8/e = 72/e (or aprox., 26.4873)

Jul 13th, 2014

Did you know? You can earn $20 for every friend you invite to Studypool!
Click here to
Refer a Friend
...
Jul 13th, 2014
...
Jul 13th, 2014
Oct 24th, 2017
check_circle
Mark as Final Answer
check_circle
Unmark as Final Answer
check_circle
Final Answer

Secure Information

Content will be erased after question is completed.

check_circle
Final Answer