1. Suppose a culture of bacteria starts with 5000 bacteria. After one hour, the count is 6000. Find an exponential equation that models the number of bacteria in hours. Keep at least 4 decimal places in your formula for rounded values. Find the doubling time of the bacteria. Round the doubling time to the nearest 0.01 hours.
2. A cup of coffee which is initially at a temperature of 157F is placed in a room which is at a constant temperature of 72C In 8 minutes, the coffee has cooled to 138C. Find the Newton's Law of Cooling formula that models the coffee's temperature in minutes. Keep at least 4 decimal places in your formula for rounded values. Determine to the nearest minute how long it will take the coffee to cool to a temperature of 100F.