Example 4: It is observed that a certain bacteria culture grows at a relative growth rate of 15% per hour. When an antibiotic is introduced, the relative growth rate changes to only 3% per hour. An initial count of 50 bacteria is put into a petri dish and monitored for 24 hours. (a) Determine the approximate size of the bacteria population if no antibiotic is present. (b) Determine the approximate size of the bacteria population if the antibiotic is present. Example 5: The rat population in a certain U.S. city was approximately 350,000 in 2009 and it was discovered that the rat population doubled every 18 years. (a) Find an exponential model of base 2 for the rat population / years since 2009. (b) Find an exponential model of base e for the rat population / years since 2009. (c) Estimate how long it takes the rat population to reach 1.5 million using both models above