Worksheet – 4.6
NAME_______________________________
1) The cost of tuition for at four-year public universities has been increasing roughly
exponentially for the past 5 years. In 1996, the average cost of tuition was $2,975 per
year. By 1997, the figure had risen to $3,211.
a. Find the equation that represents the average cost of tuition at four-year universities as
a function of time, with t  0 corresponding to 1996.
b. Use this model to estimate the average cost of tuition in 2003.
c. Find the year that the average tuition would be $10,000.
2) A radioactive substance has a half-life of 10 years.
a. Find the equation that describes the quantity of the substance present at time t using
the continuous exponential model.
b. Determine the continuous rate of decay.
c. What percentage of the original amount would remain after 22 years?
3) Suppose 80 ounces of a radioactive substance decays to 9 ounces in 9 hours. What is the
half-life of the substance?
4) Atmospheric pressure is related to height above sea level according to an exponential
model. Suppose the pressure at 18,000 feet is half that at sea level. Assuming P0 is
the pressure at sea level, determine a model for pressure h feet above sea level, and
estimate the pressure at 1000 feet.
5) A certain lake is stocked with 1000 fish. The population is growing according to the
10,000
logistics curve: P 
where t is measured in months since the lake was initially
1  9e t / 5
stocked.
a. Find the population in 8 months.
b. After how many months will the fish population be 2000?
c. Is there a maximum possible fish population that the lake can sustain? What graphical
feature is this on the graph?