SOLUTION
Since t is the number of years since 1950, we will take 1950 to be 0, then the other years in multiples of 5, since it is 5 years interval. The table and the model from a graphing calculator is shown below
From the model
[tex]\begin{gathered} R=at+b \\ b=142.091 \\ a=-1.92364 \end{gathered}[/tex]
Substituting, we have
[tex]\begin{gathered} R=-1.92364t+142.091 \\ \end{gathered}[/tex]
Hence the linear function is
[tex]R=-1.92364t+142.091[/tex]
The exponential function
From the calculator
We have
[tex]\begin{gathered} R=a(b)^t \\ a=152.398,b=0.97849 \end{gathered}[/tex]
Plugging the values we have
[tex]R=152.398(0.97849)^t[/tex]
Hence the exponential function is
[tex]R=152.398\times(0.97849)^t[/tex]
Mortality rate in 2022.
1950 to 2022 is 72 years. So we substitute 72 for t in the exponential function, we have
[tex]\begin{gathered} R=152.398\times(0.97849)^t \\ R=152.398(0.97849)^{72} \\ R=31.84448 \end{gathered}[/tex]
Hence the answer is 31.8 to one decimal place
