College Algebra

Question

In the year 2007, the age-adjusted death rate per 100,000 Americans for heart disease was 226.8. In the year 2011, the age-adjusted death rate per 100,000 Americans for heart disease had changed to 194.

a) Find an exponential model for this data, where t = 0 corresponds to 2007.    

b) Assuming the model remains accurate, estimate the death rate in 2038. (Round to the nearest tenth.)

Answer 1

This is just an exponential decay problem where Final value will equal initial value times some decay factor raised to a power. In this problem

Initial value in 2007 = 226.8

Final value in 2011 = 194

t is 4 years

We can use this information to solve for our decay factor which we will use for our general equation

194 = 226.8 x r^4

194/226.8 =r^4. Now take the fourth root of both sides to solve for r

r= .9617

So General equation is f(t) = 226.8 x (.9617)^t

To find the death rate in 2038 we end to know how many years have passed between 2007 and 2038 which is 31 years

f(31) = 226.8 x (.9617)^31= 67.588 = 67.6 rounded to nearest tenth