Statistics Projects for High School Students

Painful bone metastases are common in advanced prostate cancer. Physicians often order treatment with strontium-89 (89Sr), a radionuclide with a strong affinity for bone tissue. A patient is given a sample containing 4 mCi of ${\displaystyle {89}^{Sr}}$.
If 20% of the ${\displaystyle {89}^{Sr}}$ remains in the body after 90 days, write a function of the form ${\displaystyle Q\left(t\right)=Q0e^{-kt}}$ to model the amount Q(t) of radioactivity in the body t days after the initial dose.
b. what is the biological half-life of ${89}^{Sr}$ under this treatment? Round to the nearest tenth of a day.

Use the two-way table of data from another student survey to answer the following question.
$\begin{array}{|ccc|}\hline & LikeAerobic& Exercise\\ LikeWeightLifting& Yes& No& Total\\ Yes& 7& 14& 21\\ No& 12& 7& 19\\ Total& 29& 21& 40\\ \hline\end{array}$
Find the conditional relative frequency that a student likes to lift weights, given that the student likes aerobics.

Raul is conducting a survey for the school news blog. He surveys 200 senior-class students and finds that 78 students have access to a car on weekends, 54 students have regular chores assigned at home, and 80 students neither have access to a car, nor have regular chores to do. Raul is having a hard time putting the data into a two-way table. Car No car Chores No chores a. Copy and complete the two-way table to help Raul figure out the number of students in each situation. b. Two-way tables often include row and column totals. Your two-way table should now have row and column totals. Are these students' car privileges and their participation in regular chores related? Describe your response in light of the issue.

For the following exercises, enter the data from each table into a graphing calculator and graph the resulting scatter plots. Determine whether the data from the table could represent a function that is linear, exponential, or logarithmic.

$\begin{array}{|ccccccccccc|}\hline x& 1.25& 2.25& 3.56& 4.2& 5.65& 6.75& 7.25& 8.6& 9.25& 10.5\\ f(x)& 5.75& 8.75& 12.68& 14.6& 18.95& 22.25& 23.75& 27.8& 29.75& 33.5\\ \hline\end{array}$

Maurice and Lester are twins who have just graduated from college. They have both been offered jobs where their take-home pay would be $2500 per month. Their parents have given Maurice and Lester two options for a graduation gift. Option 1: If they choose to pursue a graduate degree, their parents will give each of them a gift of $35,000. However, they must pay for their tuition and living expenses out of the gift. Option 2: If they choose to go directly into the workforce, their parents will give each of them a gift of $5000. Maurice decides to go to graduate school for 2 years. He locks in a tuition rate by paying $11,500 for the 2 years in advance, and he figures that his monthly expenses will be $1000. Lester decides to go straight into the workforce. Lester finds that after paying his rent, utilities, and other living expenses, he will be able to save $200 per month. Their parents deposit the appropriate amount of money in a money market account for each twin. The money market accounts are currently paying a nominal interest rate of 3 percent, compounded monthly. At the end of 2 years, Lester receives a raise and decides to save $250 each month. Maurice receives a $5000 graduation gift from his parents and deposits this amount into his money market account. Maurice goes to work and saves $500 each month. Complete the equations below for the money market account balance for each twin. Let the initial balance u0 be the account balance at the end of 2 years. Write an expression for this month's account balance un in terms of un−1. Recall that the interest rate for the account is 3 percent, compounded monthly. Maurice:$u_0=\mathrm{\$}5248.47,u_n=\text{\_\_\_\_\_.}\text{Lester}:u_0=\text{\_\_\_\_\_},u_n=\text{\_\_\_\_\_}.$