Question

Biologists are treating a lake contaminated with bacteria. The level of contamination is changing at a rate of dN/dt=-1110/t² -230 bacteria per

cubic centimeter per day, where is the number of days since treatment began. Find a function N(t) to estimate the level of contamination if the
level after I day was 5380 bacteria per cubic centimeter.

Answer 1

Answer: the function N(t) to estimate the level of contamination in the lake is:

N(t) = -1110 ln(t) - 230t + 1110 ln(I) + 230I + 5380

Step-by-step explanation: ∫ dN/dt dt = ∫ (-1110/t² -230) dt

N(t) = -1110 ln(t) - 230t + C

N(I) = -1110 ln(I) - 230I + C = 5380

C = 1110 ln(I) + 230I + 5380