Chapter 4.2, Problem 5E

Reminder Round all answers to two decimal places unless otherwise indicated.

Theater Production Data from the Statistical Abstract of the United States show that in $1995$, there were $56.61$ thousand performances in the United States by nonprofit professional theaters. From $1995$ through $2007$, this number increased on average by about $10\%$ each year.

a. Let P denote the number of performances, in thousands, and let $t$ denote the time in years since $1995$. Make an exponential model for P versus $t$.

b. How many performances by non-profit professionals theaters does your model give for $2007$? (The actual number was $197$ thousand.)