Chapter 4.9, Problem 3AYU

Advanced-Stage Breast Cancer The data in the table below represent the percentage of patients who have survived after diagnosis of advanced-stage breast cancer at 6-month intervals of time.

(a) Using a graphing utility, draw a scatter diagram of the data with time after diagnosis as the independent variable.

(b) Using a graphing utility, build an exponential model from the data.

(c) Express the function found in part (b) in the form $A(t)=A_{{}_0}{e}^{kt}$.

(d) Graph the exponential function found in part (b) or (c) on the scatter diagram.

(e) What percentage of patients diagnosed with advanced-stage cancer are expected to survive for 4 years after initial diagnosis?

(f) Interpret the meaning of $k$ in the function found in part (c).