One measure of living standards in country $A$ is given by the following formula.
\[
L(t)=8+4 e^{0.19 t}
\]
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: \(L(t)=8+4 e^{0.19 t}\), 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 \(L(5) = 8 + 4e^{0.19*5}\), \(L(14) = 8 + 4e^{0.19*14}\), and \(L(20) = 8 + 4e^{0.19*20}\).

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 \(\boxed{18.34}\). (b) For the year 1996, \(L(t)\) is approximately \(\boxed{65.19}\). (c) For the year 2002, \(L(t)\) is approximately \(\boxed{186.8}\).