Question

the concentration of a certain drug in the bloodstream t hours after the drug is administered is given by c(t)=35te^(-bt) ng/ml, where b is some positive constant. suppose that the drug reaches maximum concentration exactly seven hours after being administered.Find the constant b.

Answer 1

is this calculus ?

Answer 2

Yes

Answer 3

did you find the derivative of c(t) with respect to "t" ?

Answer 4

is this calculus ?

Answer 5

did you find the derivative of c(t) with respect to "t" ?

Answer 6

-35e^(-bt) bt + 35e^(-bt)

Answer 7

the standard technique to finding a min/max is to set the derivative to zero
and in this case , solve for b

Answer 8

and use
drug reaches maximum concentration exactly seven hours
set t= 7, so you get a numerical value for b

Answer 9

the standard technique to finding a min/max is to set the derivative to zero
and in this case , solve for b

Answer 10

I did that and had something like -35e^(-7b) 7b + 35e^(-7b) which factors to
(35e^(-7b)) (-7b+1)

Answer 11

yes, and see that equal to 0

Answer 12

-7b+1 =0 gives me b=0.1428 but i couldn't solve 35e^(-7b) = 0

Answer 13

the standard technique to finding a min/max is to set the derivative to zero
and in this case , solve for b

Answer 14

yes, b= 1/7

the other factor can be ignored (in theory, b= infinity makes it approach zero, but we can't use that)

Answer 15

Here is a graph of your function, with b= 1/7. As you can see, it peaks at x=7
(I used x instead t to plot it)

Answer 16

ok thanks

Answer 17

yw