Solve the Problem $\mathrm{x}=0$ Correspond to 1970 And $\mathrm{x}=20$ To 1990 Find the Rule of a Piecewise Linear Function

Solve the problem.
-The population of one city (in thousands) was 82.2 in 1970, 95.1 in 1980, and 102.1 in 1990. Let $\mathrm{x}=0$ correspond to 1970 and $\mathrm{x}=20$ to 1990 . find the rule of a piecewise linear function $\mathrm{f}$ that models this data, that is a piecewise function with $\mathrm{f}(0) =82.2, \mathrm{f}(10) =95.1$ , and $\mathrm{f}(20) =102.1$ .

A) $f(x) = \begin{cases}1.29 x+82.2 & \text { if } 0 \leq x \leq 10 \\ 0.70 x+95.1 & \text { if } 10 \leq x \leq 20\end{cases}$
B) $f(x) = \begin{cases}1.29 x+82.2 & \text { if } 0 \leq x \leq 10 \\ 0.70 x+88.1 & \text { if } 10 \leq x \leq 20\end{cases}$
C) $f(x) = \begin{cases}1.29 x+82.2 & \text { if } 0 \leq x \leq 10 \\ 1.00 x+85.1 & \text { if } 10 \leq x \leq 20\end{cases}$
D) $f(x) =5.055 x+82.2$