the concentration C of a chemical

Question

The concentration C of a chemical in the bloodstream t hours after injection into muscle tissues is given by the following.

C(t)= 7t/(27+t³)

(a) Complete the table and use it to approximate the time when the concentration is greatest. (Round your answers to three decimal places.)

t	0	0.5	1	1.5	2	2.5	3
C(t)

t ≈______  hr

(b) Use a graphing utility to graph the concentration function and use the graph to approximate the time when the concentration is the greatest.

t ≈ ______ hr

(c) Use calculus to determine analytically the time when the concentration is greatest.

t = ______ hr

Answer 1

0=

dC/dt=

[7(t^3 + 27) - (7t)(3t^2)] / (t^3 + 27)^2

the denominator cancels, not a factor, and irrelevant

[7(t^3 + 27) - (7t)(3t^2)] = 0

7 t^3 + 27*7 - 21t^3 = 0

-14t^3 + 189 = 0

2t^3 - 27 = 0

t^3 = +27/2

t = +3 / 2^(1/3)

= +3 * 2^(2/3) / 2

= (-3/2)(2^(2/3))

APPROXIMATELY (2.381, 0.41)