For 1 - 4, use the following situation:
A potato is put into an oven that has been heated to 350° F. Its temperature as a function of time is given by
T (t ) = a (1 - e^-kt ) + b . The potato was 50° F when it was first put into the oven.
1. What is the value of b in this context? Explain.
2. What is the value of a in this context? Explain.
3. If the potato is 60° F after 2 minutes, what is the value of k ? Explain.
4. When will the potato reach 150° F? Explain.
For 5 - 9, use the following situation:
The number of people in a town of 10,000 who have heard a rumor started by a small group of people is given by the following function:
N (t ) = 10,000/(5 + 1245e^-.97t )
5. How many people were in the group that started the rumor?
6. How many people have heard the rumor after 1 day? After 5 days?
7. How long before 1,000 of the people in the town have heard the rumor?
8. Sketch the graph of this function and mark the places that answer the questions in 5 - 7.
Use the graph below to answer questions 9 and 10.
9. If this graph represents the growth of a fish population that was introduced into a small lake in 2002, how
many fish were originally put into the pond?
10. What is the carrying capacity of the lake for this population of fish?
20. If the function for the graph in questions 18 and 19 is P (t ) = 1200/1 + 11 e^-.2t , which of the following could
be the graph of P (t ) = 1200/1 + 11e^-.8t ?
Write the letter: _______