Question 190335
<font face="Tahoma" size=1.5>
</pre><font size=4><b>
a) okay you got points given in 1995 & 2000 --> (5,24.5) & (10,25.1), where we can find the slope=m via Point Slope Form.


{{{m=(y[2]-y[1])/(x[2]-x[1])=(25.1-24.5)/(10-5)=0.60/5=red(0.12)}}}, too small I guess.


Then thru point (5,24.5), via Slope-Intercept Form, {{{y=mx+b}}} with {{{ m=0.12}}}:


{{{24.5=(0.12)(5)+b}}} ----> {{{24.5=0.60+b}}}
{{{b=24.5-0.60=red(23.9)}}}, y-Intercept


So our line eqn ----> <font color=blue>y=0.12x+23.90</font> or <font color=blue>-0.12x+y=23.90</font>, Std Form



b) <font color=blue>x</font>, represent the year, and <font color=blue>y</font>, represent the age.




c)As we calculated, the Slope=m being <font color=blue>0.12</font>. Remember {{{Slope=DELTA(y)/DELTA(x)=(y*axis)/(x*axis)=(up*down)/(left*right)=0.12/1}}}.


Meaning, the age will increased by {{{(0.12cross(yr))(12mo/1cross(yr))=1.44}}}. That is <font color=blue> 1 month</font> and {{{(.44cross(month))(30days/1cross(month))= 13.2}}} =<font color=blue>13 days</font> and {{{(0.2cross(day))(24hrs/1cross(day))=4.8}}}=<font color=blue>4 hours</font> and {{{(0.8cross(hr))(60sec/1cross(hr))}}}=<font color=blue>48 seconds</font> in <font color=red>1 year</font>.





d)when y=30, we'll do interpolation.


<font color=blue>A</font>=1995=5 ------- <font color=blue>D</font>=24.5
<font color=blue>B</font>=2000=10 ------ <font color=blue>E</font>=25.1
<font color=blue>C</font>=<font color=red>x</font> --------------- <font color=blue>F</font>=30


{{{(A-B)/(A-C)=(D-E)/(D-F)}}}
{{{(5-10)/(5-x)=(24.5-25.1)/(24.5-30)}}} ---> {{{(-5)/(5-x)=(-0.60)/(-5.5)}}}Cross multiply,
{{{(-0.60)(5-x)=(-5)(-5.5)}}}
{{{-3+0.60x=27.5}}}
{{{0.60x=27.5+3=30.50}}} -----> {{{cross(0.60)x/cross(0.60)=cross(30.50)50.833333/cross(0.060)}}}
{{{x=50.833333}}} ---> That is in<font color=blue> year 2050 </font>and {{{(0.833333cross(yr))(12months/1cross(yr))}}}= and <font color=blue>10 months</font>



e) It's good to see the graph,


{{{drawing(500,500,-10,60,-10,35,graph(500,500,-10,60,-10,35,0.12x+23.90),green(line(0,30,50.833333,30)),green(line(50.83333,30,50.833333,0)),red(locate(2,32,Age=30)),red(locate(46,2,2050*10months)),arrow(18,25,18,22),green(locate(17,21,y=0.12x+23.90)),green(line(5,0,5,24.5)),green(line(5,24.5,0,24.5)),red(locate(2,24,Age=24.5)),red(locate(2,2,2005)),green(line(0,25.1,10,25.1)),green(line(10,25.1,10,0)),red(locate(2,27,Age=25.1)),red(locate(9,2,2010)),green(locate(20,-2,YEAR)),green(locate(-8,30,AGE)))}}}


Thank you,
Jojo</font>