One treatment of Roche’s Tamiflu, a drug that reduced the severity of bird flu symptoms, is usually 10 pills taken over five days. Tamiflu production was 5.5 million treatments in 2002 and has approximately doubled each year since then. (Source: Roche) a.
Let n = g(t) be the number of treatments (in millions) produced in the year that is t years since 2002.
Find an equation of g. b.
What is the n-intercept of the model? What does it mean in this situation? c.
Predict the number of treatments that will be produced in 2005. d.
Roche plans to produce 300 million treatments in 2007. If that happens, will production continue to double each year from 2002 to 2007? Explain.
The revenue from ring tones was $91 million in 2003 and has grown by about 114% per year since then
(Source: Jupiter Research).
That is, each year the revenue is about 2.14 times the previous year’s revenue. a.
Let r = h(t) be the revenue (in millions of dollars) from ring tones in the year that is t years since 2003.
Find an equation of h. b.
What is the r-intercept of the model? what does it mean in this situation? c.
What is the base b of ( ) a b t
? What does it mean in this situation? d.
Predict the revenue from ring tones in 2009. e.
Jupiter Research predicts that revenue from ring tones will be $724 million in 2009. If that happens, will each year’s revenue continue to be 2.14 times the revenue of the previous year? Explain
Someone invests $3000 in an account at 8% interest compounded annually. let f(t) be the value (in dollars) of the account at t years after she has invested the $3000. a.
Find an equation of f. b.
What is the base b of ( ) a b t
? What does it mean in this situation? c.
What is the coefficient a of your model ( ) a b t
? d.
What will be the account value in 15 years?
A thyroid cancer patient ingests a signle dose of radioactive iodine-131 to kill the cancer cells. Iodine-131 has an effective half-life or 7.56 days – some is lost to radioactive decay, and some is removed through urination.
Let f(t) be the percentage of the iodine-131 that remains in the patient’s body at t days since the ingested the iodine-131. a.
Find an equation of f. b.
For 3 days after ingesting the iodine-131, the patient must stay at least 1 meter away from other people, because the radiation he emits coud be harmful. What percentage of the iodine-131 will remain in his body after 3 days? c.
The patient can safely spend a lot of time near a child when at most 5% of the iodine-131 remains. Use
“intersect” on the graphing calculator to estimate when that time will be.

A person invests $6000 in an account at 10% interest compounded annually. When will the value of the investment be doubled? Explain why it will take less than 10 years, even thought the rate is 10%?
The number of Starbucks stores worldwide at t years since 1990 is given by f t
 t
, where f(t) is the number of Starbucks stores worldwide at t years since 1990 a. Estimate when the first Starbucks store opened. b. The first store opened in 1971 in Seattle, Washington. Do you think the number of stores grew exponentially at the beginning? c. What is the base of our model in the exponential equation? What does it mean in this situation? d. Predict when there will be an average of 500 Starbucks stores in each country (there are 192 countries). e. Predict when there will be one store for every person in the world? Assume a world population of 8.6 billion.
Comment about model breakdown.
A mummy was on display at a museum in Niagara Falls until it was sold in 1990. A few years later, researchers identified the mummy as the ancient Egyptian pharaoh Rameses I. The mummy was eventually returned to
Egypt. If 69.57% of the carbon-14 in the mummy remains, estimate how long ago Rameses I lived. The half-life of carbon-14 is 5730 years.
A person makes a cup of tea. The tea’s temperature y (in degrees Fahrenheit) is given by y
  e

0.05
t where t is the number of minutes since the person made the tea. a. What was the temperature of the tea when the person made it? b. If the person waits 5 minutes to begin drinking the tea, what is the temperature of the tea then? c. The tea is lukewarm at a temperature of about 98.6
o
F . If the person lets the tea sit until it is lukewarm, how much time has gone by since she made the tea?