In the year 1997, the age-adjusted death rate per 100,000 Americans for heart disease was 248.2. In the year 1998, the age-adjusted death rate per 100,000 Americans for heart disease had changed to 241.3. a) Find an exponential model for this data, where $t=0$ corresponds to 1997. \[ f(t)= \] b) Assuming the model remains accurate, estimate the death rate in 2032. (Round to the nearest tenth.)

Step 1 ：We are given two data points (0, 248.2) and (1, 241.3) and we are asked to find an exponential model of the form \(f(t) = ab^t\) where \(t=0\) corresponds to 1997.

Step 2 ：To find the values of \(a\) and \(b\), we can use the two given data points.

Step 3 ：From the first data point (0, 248.2), we can see that when \(t=0\), \(f(t)=248.2\). This gives us the equation \(a = 248.2\).

Step 4 ：From the second data point (1, 241.3), we can see that when \(t=1\), \(f(t)=241.3\). This gives us the equation \(248.2b = 241.3\).

Step 5 ：We can solve this system of equations to find the values of \(a\) and \(b\). The solution to the system of equations is \(a = 248.2\) and \(b \approx 0.9722\).

Step 6 ：Therefore, the exponential model for this data is \(f(t) = 248.2(0.9722)^t\).

Step 7 ：Now, we need to estimate the death rate in 2032. Since \(t=0\) corresponds to 1997, \(t=2032-1997=35\) corresponds to 2032.

Step 8 ：We can substitute \(t=35\) into the model to find the estimated death rate in 2032. The estimated death rate in 2032 is \(\boxed{92.5}\) per 100,000 Americans.