<PRE><B>Question 1153986</B>
&lt;br&gt;
{{{C = at^2+bt+c}}}&lt;br&gt;
where t=0 corresponds to 1962.&lt;br&gt;
data:&lt;br&gt;&lt;pre&gt;
   year   t     C
  ----------------
   1962   0    319
   1982  20    340
   2002  40    368&lt;br&gt;&lt;/pre&gt;
(a) determine the coefficients a, b, and c and write the equation&lt;br&gt;&lt;pre&gt;
Equations:&lt;br&gt;
{{{c = 319}}}  [1]
{{{400a+20b+c = 340}}}  [2]
{{{1600a+40b+c = 368}}}  [3]&lt;br&gt;
{{{400a+20b = 21}}}  [4] (from [1] and [2])
{{{1600a+40b = 49}}}  [5] (from [1] and [3]&lt;br&gt;
{{{800a+40b = 42}}}  [6] ([4], doubled)&lt;br&gt;
{{{800a = 7}}}  ([5]-[6])
{{{a = 7/800}}}  [7]&lt;br&gt;
{{{14+40b = 49}}}  (from [5] and [7])
{{{40b = 35}}}
{{{b = 7/8}}}&lt;br&gt;&lt;/pre&gt;
ANSWERS:
a = 7/800
b =7/8
c = 319
{{{C = (7/800)t^2+(7/8)t+319}}}&lt;br&gt;
(b) Find the year when C = 2(319) = 638&lt;br&gt;
{{{(7/800)t^2+(7/8)t+319 = 638}}}&lt;br&gt;
Solving algebraically is certainly possible, but very tedious.&lt;br&gt;
Graph the function and the constant 638 on a graphing calculator and find where they intersect.&lt;br&gt;
A graph:&lt;br&gt;
{{{graph(400,400,-50,200,-100,800,(7/800)x^2+(7/8)x+319,638)}}}&lt;br&gt;
The intersection of the two graphs, to the nearest whole number, is 147, indicating the year 1962+147 = 2109.&lt;br&gt;
ANSWER: year 2109&lt;br&gt;
</PRE>