One measure of living standards in country $A$ is given by the following formula.
$$L(t)=8+4e^{0.19t}$$
In this formula $t$ is the number of years since 1982. Find $L$ to the nearest hundredth for each year.
(a) 1987
(b) 1996
(c) 2002

Step 1 ：The problem provides us with a formula for living standards in country A: $L(t)=8+4e^{0.19t}$, where $t$ is the number of years since 1982. We are asked to find $L(t)$ for the years 1987, 1996, and 2002.

Step 2 ：To find these values, we need to substitute the corresponding $t$ values into the formula. The $t$ value is the number of years since 1982, so for 1987, $t=1987-1982=5$, for 1996, $t=1996-1982=14$, and for 2002, $t=2002-1982=20$.

Step 3 ：Substituting these $t$ values into the formula, we get $L(5)=8+4e^{0.19\ast 5}$, $L(14)=8+4e^{0.19\ast 14}$, and $L(20)=8+4e^{0.19\ast 20}$.

Step 4 ：Calculating these expressions, we find that $L(5)$ is approximately 18.34, $L(14)$ is approximately 65.19, and $L(20)$ is approximately 186.8.

Step 5 ：Final Answer: (a) For the year 1987, $L(t)$ is approximately $\boxed{{\displaystyle 18.34}}$. (b) For the year 1996, $L(t)$ is approximately $\boxed{{\displaystyle 65.19}}$. (c) For the year 2002, $L(t)$ is approximately $\boxed{{\displaystyle 186.8}}$.