1.

In 2011 a country's federal receipts (money taken in) totaled $2.23 trillion. In 2013, total federal receipts were $2.92

trillion. Assume that the growth of federal receipts, F, can be modeled by an exponential function and use 2011 as the base year

(t=0).

a)	Find the growth rate k to six decimal places, and write the exponential function F(t), for total receipts in trillions of dollars.
b)	Estimate total federal receipts in 2015.
c)	When will total federal receipts be $9 trillion?

2.

Suppose that in 1620, a man bought a diamond for $22. Suppose that the man had instead put the $22 in the bank at

3% interest compounded continuously. What would that $22 have been worth in 2004?

In 2004, the $22 would have been worth $?

3.

a)	The cost of first-class postage stamp was 5 in 1961 and 55 in 2010. This increase represents exponential growth. Write the function S for the cost of a stamp t years after 1961 (t=0).
b)	What was the growth rate in the cost?
c)	Predict the cost of a first-class postage stamp in 2015, 2018, and 2021.
d)	The Forever Stamp is always valid as first-class postage on standard envelopes weighing 1 ounce or less, regardless of any subsequent increases in the first-class rate. An advertising firm spent $5500 on 10,000 first-class postage stamps in 2009. Knowing it will need 10,000 first-class stamps in each of the years 2010-2022, it decides at the beginning of 2010 to try to save money by spending $5500 on 10,000 Forever Stamps, but also buying enough of the stamps to cover the years 2011 through 2022. Assuming there is a postage increase in each of the years 2015, 2018, and 2021 to the cost predicted in part (c), how much money will the firm save by buying the stamps?

4.

The size of a certain insect population is given by P(t)=500e.01t, where t is measured in days. At what time will the population equal 2500?

It will take (?) days for the population to equal 2500?

5.

A chemical substance has a decay rate of 6% per day. The rate of change of an amount N of the chemical after t days is given by dNdt=0.060N.

a) Let N0 represent the amount of the substance present at t=0. Find the exponential function that models the decay.b) Suppose that 800 g of the substance is present at t=0. How much will remain after 5 days?

c) What is the rate of change of the amount of the substance after 5 days?

d) After how many days will half of the original 800 g of the substance remain?

6.

Find the present value of $2000 payable at the end of 4 years, if money may be invested at

6% with interest compounded continuously.

The present value of $2000 is $(?)

7.

The concentration of a drug in the body decreases exponentially after a dosage is given. In one clinical study, adult subjects averaged 13 micrograms/milliliter (mcg/mL) of the drug in their blood plasma 1 hr after a 1000-mg dosage and 3 micrograms/milliliter 7 hr after dosage.

a) Find the value k, and write an equation for an exponential function that can be used to predict the concentration of the drug, in micrograms/milliliter, t hours after a 1000-mg dosage.

b) Estimate the concentration of the drug 2 hr after a 1000-mg dosage.

c) To relieve a fever, the concentration of the drug should go no lower than 3 mcg/mL. After how many hours will a 1000-mg dosage drop to that level?

8.

The population of a country dropped from 52.6 million in 1995 to 45.5 million in 2009. Assume that P(t), the population, in millions, t years after 1995, is decreasing according to the exponential decay model.

a) Find the value of k, and write the equation.

b) Estimate the population of the country in 2018.

c) After how many years will the population of the country be 3 million, according to this model?

9.

A coroner arrives at a murder scene at 11 p.m. She finds the temperature of the body to be 83.2F. She waits one hour, takes the temperature again, and finds it to be 79.9F. She notes that the room temperature is 66F. Assuming that the temperature of the body was 98.6F when the murder occured, when was the murder committed?

The murder was commited at approximately (?)