Darryl wants to add enough water to 8 gallons of a 10% bleach solution to make a 5% bleach solution. Which equation can he use to find x, the number of gallons of water he should add? Original (Gallons) Added (Gallons) New (Gallons) Amount of Bleach 0.8 0 0.8 Amount of Solution 8 x 8 + x StartFraction 0.8 Over 8 + x EndFraction times StartFraction 5 Over 100 EndFraction = 1 StartFraction 0.8 Over 8 + x EndFraction times = StartFraction 5 Over 100 EndFraction StartFraction 0.8 Over 8 + x EndFraction = StartFraction 100 Over 5 EndFraction StartFraction 0.8 Over 8 + x EndFraction divided by StartFraction 5 Over 100 EndFraction = 1

The biologist has a second culture to examine. she knows that the population of the culture doubles every 15 minutes. after 1 hour and 15 minutes, her assistant found that 80,000 bacteria were present. a) what was the size of the initial population? b) predict the size of the culture at t=3 hours. what was the size of the population at 40 minutes? explain and justify your answers. c) create a graph of the population as a function of time. find an equation that can be used to predict the size of the population at any time t. d) examine the rate at which the bacteria culture is growing. how fast is the culture growing after 1 hour? after 1.5 hours? after 2 hours? use a time interval of h = 0.01 hours to estimate these rates. interpret these rates in terms of the context of the problem situation. how do these three rates compare?