Question 490262
The following is an exponential relationship between unemployment rate, U, and inflation rate, I depicted by the function
I = 24e^(-0.3U)
a. Sketch a graph of this function, for domain 0 ≤ U ≤ 10 
Rewrite the given equation using x & y, more understandable for graphing it
y = 24e^(-.3x)
They want us to plots this for x=0 to x=10, using a calc, substitute values for x and find y using the given equations, round to the nearest 10th
:
 x | y
-------
 0| 24;;;    y = 24*e^(-.3*0)"
 1| 17.8;  y = 24*e^(-.3*1)
 2| 13.2;  y = 24*e^(-.3*2)
 4| 7.2;;   y = 24*e^(-.3*4)
 6| 4.0;;   y = 24*e^(-.3*6)
 8| 2.2;;  y = 24*e^(-.3*8)
10| 1.2;;  y = 24*3^(-.3*10)
:
Plot these x/y points, it should look like this:
{{{ graph( 300, 200, -4, 12, -10, 28, 24*e^(-.3x)) }}} 
:
:
b. Rearrange the formula for the above function to make U the subject.
I = 24*e^(-.3u)
divide both sides by 24, and write it:
{{{e^(-.3u)}}} = {{{I/24}}}
Find the natural log of both sides
{{{ln(e^(-.3u))}}} = {{{ln(I/24)}}}
using the log equiv of exponents
{{{-.3u*ln(e)}}} = {{{ln(I/24)}}}
the ln of e is 1, so we can write it;
-.3u = {{{ln(I/24)}}}
divide both sides by -.3
u = {{{-1/.3}}}*{{{ln(I/24)}}}
or using decimals we can write it
u = {{{-3.33*ln(I/24)}}}