Originally Posted by

**skeske1234** A swimming pool is treated periodically to control the growth of bacteria. Suppoe that t days after a treatment, the concentration of bacteria per cubic cm is **C(t)=30t^9-240t+500**. Find the lowest concentration of bacteria during the first week after the treatment.

C(t) = 30t^2 - 240t + 500 instead of 30t^9 ... ?

Ok.. what I did.. I think i did right, but the back of the book.. just wondering if they are wrong. Just making sure, please confirm with me.

My work is below:

c'(t)=60t-240

critical numbers

c'(t)=0 when 60t-240=0

t=4

domain

0<=t<=7

test

f(4)=0 C(4) = 20

f(0)=-240 C(0) = 500

f(7)=180 C(7) = 290

therefore the lowest concentration of bacteria during the first week after the treatment is 0 cm^3 on the 4th day

That is my answer. However, the back of the book says.. 20