1) In 1991, the cost of mailing a 1 oz. first-class letter was 29 cents, and the inflation rate was 4.6%. If the inflation rate stayed constant, the function C (t) = .29(1.046)^t would represent the cost of mailing a first-class letter as a function of years since 1991.
1. If the function given holds true, in what year would the cost of mailing a first-class letter reach 60 cents?
2. In 2007, the cost of mailing a first-class letter was 41 cents. Has the inflation rate stayed constant since
1991? Explain.
2) Use the following situation:
A hot bowl of soup cools according to Newton's law of cooling. Its temperature (in degrees Fahrenheit) at time
t is given by T (t ) = 68 + 144e^-.04t , where t is given in minutes.
i. What was the initial temperature of the soup?
2. What is the temperature of the soup after 15 minutes?
3. How long after serving is the soup 125° F?
3) A forensic detective is called to the scene of a murder at 2 a.m. When she checks the temperature of the body, she finds that it is 80° F. The temperature of the room in which the body is found is 65° F. If the detective uses Newton's law of cooling, T (t ) = TA + (T0 - TA) )e^-0.1947t , what will she say was the time of death?
4) An archeologist finds an artifact that contains 44% of the carbon-14 that it would have had originally. What is the estimated age of the artifact? (The half-life of carbon-14 is 5,730 years.)
5) Use the following situation:
A population of bacteria begins with 1,500 bacteria and grows to 4,500 in one hour.
1. Find a function that represents the growth of this culture of bacteria as a function of time.
2. How long does it take this culture of bacteria to double?