Please help The American College of Sports Medicine considers age as one factor when it recommends low and
high heart rates during workout sessions.
For safe and efficient exercise, your heart rate should be between 55% and 90% of the maximum
heart rate level. The maximum heart rate is calculated by subtracting a person's age from 220
beats per minute.
(Let a represent a person's age and h represent the person's recommended heart rate.)
1. The following equation represents the low value for heart rate. Simplify the equation.
h = .55(220-a)
2. The following equation represents the high value for heart rate. Simplify the equation.
h = .90(220-a)
3. Use these two expressions to write a system of inequalities that represents the heart rate range
for safe and efficient exercise. (Hint: you need to write two separate inequalities)

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?