Question

See attached pic for problem. Just need parts C and D

Answer 1

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

`\begin{gathered} R=at+b \\ b=142.091 \\ a=-1.92364 \end{gathered}`

Substituting, we have

`\begin{gathered} R=-1.92364t+142.091 \\ \end{gathered}`

Hence the linear function is

`R=-1.92364t+142.091`

The exponential function

From the calculator

We have

`\begin{gathered} R=a(b)^t \\ a=152.398,b=0.97849 \end{gathered}`

Plugging the values we have

`R=152.398(0.97849)^t`

Hence the exponential function is

`R=152.398*(0.97849)^t`

Mortality rate in 2022.

1950 to 2022 is 72 years. So we substitute 72 for t in the exponential function, we have

`\begin{gathered} R=152.398*(0.97849)^t \\ R=152.398(0.97849)^(72) \\ R=31.84448 \end{gathered}`

Hence the answer is 31.8 to one decimal place