Question 86388
a)

{{{A=p(1+r/n)^(n*t)}}} Start with the given equation


{{{A=1(1+0.08/1)^(1*t)}}}  Plug in p=1, r=0.08, and n=1

Let t=0 and plug it into  {{{A=1(1+0.08/1)^(1*t)}}}

{{{A=1(1+0.08/1)^(1*0)}}}       Start with the given expression
{{{A=1(1+0.08)^(1*0)}}}     Divide 0.08 by 1 to get 0.08
{{{A=1(1+0.08)^(0)}}}     Multiply the exponents 1 and 0 to get 0
{{{A=1(1.08)^(0)}}}       Add 1 and 0.08 to get 1.08
{{{A=1(1)}}}      Raise 1.08 to 0 to get 1
{{{A=1}}}       Multiply 1 and 1 to get 1

So our 1st point is (0,1)
                              
Let t=1 and plug it into  {{{A=1(1+0.08/1)^(1*t)}}}

{{{A=1(1+0.08/1)^(1*1)}}}       Start with the given expression
{{{A=1(1+0.08)^(1*1)}}}     Divide 0.08 by 1 to get 0.08
{{{A=1(1+0.08)^(1)}}}     Multiply the exponents 1 and 1 to get 1
{{{A=1(1.08)^(1)}}}       Add 1 and 0.08 to get 1.08
{{{A=1(1.08)}}}      Raise 1.08 to 1 to get 1.08
{{{A=1.08}}}       Multiply 1 and 1.08 to get 1.08

So our 2nd point is (1,1.08)
                              
Let t=2 and plug it into  {{{A=1(1+0.08/1)^(1*t)}}}

{{{A=1(1+0.08/1)^(1*2)}}}       Start with the given expression
{{{A=1(1+0.08)^(1*2)}}}     Divide 0.08 by 1 to get 0.08
{{{A=1(1+0.08)^(2)}}}     Multiply the exponents 1 and 2 to get 2
{{{A=1(1.08)^(2)}}}       Add 1 and 0.08 to get 1.08
{{{A=1(1.1664)}}}      Raise 1.08 to 2 to get 1.1664
{{{A=1.1664}}}       Multiply 1 and 1.1664 to get 1.1664

So our 3rd point is (2,1.1664)
                              
Let t=3 and plug it into  {{{A=1(1+0.08/1)^(1*t)}}}

{{{A=1(1+0.08/1)^(1*3)}}}       Start with the given expression
{{{A=1(1+0.08)^(1*3)}}}     Divide 0.08 by 1 to get 0.08
{{{A=1(1+0.08)^(3)}}}     Multiply the exponents 1 and 3 to get 3
{{{A=1(1.08)^(3)}}}       Add 1 and 0.08 to get 1.08
{{{A=1(1.259712)}}}      Raise 1.08 to 3 to get 1.259712
{{{A=1.259712}}}       Multiply 1 and 1.259712 to get 1.259712

So our 4th point is (3,1.259712)
                              
Let t=4 and plug it into  {{{A=1(1+0.08/1)^(1*t)}}}

{{{A=1(1+0.08/1)^(1*4)}}}       Start with the given expression
{{{A=1(1+0.08)^(1*4)}}}     Divide 0.08 by 1 to get 0.08
{{{A=1(1+0.08)^(4)}}}     Multiply the exponents 1 and 4 to get 4
{{{A=1(1.08)^(4)}}}       Add 1 and 0.08 to get 1.08
{{{A=1(1.36048896)}}}      Raise 1.08 to 4 to get 1.36048896
{{{A=1.36048896}}}       Multiply 1 and 1.36048896 to get 1.36048896

So our 5th point is (4,1.36048896)
                              
b)


Here is a table of all of our points:

<pre>
<TABLE width=500>

<TR><TD> x</TD><TD>y</TD></TR>


<TR><TD> 0</TD><TD>1</TD></TR> 
<TR><TD> 1</TD><TD>1.08</TD></TR> 
<TR><TD> 2</TD><TD>1.1664</TD></TR> 
<TR><TD> 3</TD><TD>1.259712</TD></TR> 
<TR><TD> 4</TD><TD>1.36048896</TD></TR> 
</TABLE>
</pre> 

So lets graph these points and connect them


{{{drawing(500,500,-5,5,-5,5,
graph( 500, 500, -5, 5, -5, 5,1(1+0.08/1)^(1*x)),
grid(1),
circle(0,1,0.08),
circle(0,1,0.05),
circle(1,1.08,0.08),
circle(1,1.08,0.05),
circle(2,1.1664,0.08),
circle(2,1.1664,0.05),
circle(3,1.259712,0.08),
circle(3,1.259712,0.05),
circle(4,1.36048896,0.08),
circle(4,1.36048896,0.05)
)}}}