The table shows the age-adjusted death rates per 100,000 citizens for heart disease in a certain country. Complete parts (a) through (c) below.
(a) Find an exponential model of the form f(t) = y_0b^t for these data, where t = 0 corresponds to the year 2000. If you do not have suitable technology, use the first and last data points to find a function. If you have a graphing calculator or other suitable technology, use exponential regression to find a function.
Year: 2000, 2002, 2004, 2006, 2008, 2010, 2012, 2014
Death Rate: 256.3, 239.2, 218.0, 210.5, 186.2, 177.1, 170.1, 166.0
f(t) = (Round to two decimal places as needed.)
(b) Assuming the model remains accurate, estimate the death rate in 2020 and 2026.
The death rate in 2020 will be people per 100,000. (Round to one decimal place as needed.)
The death rate in 2026 will be people per 100,000. (Round to one decimal place as needed.)
(c) Use a graphing calculator (or trial and error) to determine the first full year in which the death rate will be below 100.
The first full year in which the death rate will be below 100.