Question 1160114
If f(x) is an exponential function where f(1)=10 and f(6.5)=90, then find the value of f(1.5), to the nearest hundred.
:
Using the form a*b^x = y
x=1, y=10
{{{a*b^1 = 10}}}
ab = 10
a = 10/b
:
x=6.5, y=90
{{{a*b^6.5 = 90}}}
replace a with 10/b
{{{10/b}}}*{{{b^6.5 = 90}}}
10*{{{b^5.5 = 90}}}
divide both sides by 10
{{{b^5.5 = 9}}}
using natural logs
5.5*ln(b) = ln(9)
ln(b) = {{{ln(9)/5.5}}}
using your calc
ln(b) = .3995
b = 1.491
find a
a = 10/1.491
a = 6.707
the equation
f(x) = {{{6.707*1.491^x}}}
:
"find the value of f(1.5), to the nearest hundred.
f(x) = {{{6.707*1.491^1.5}}}
using your calc
f(1.5) = 12.21
:
looks like this
{{{ graph( 300, 200, -4, 10, -10, 100, 6.707*1.491^x, 12.21, 90) }}}
green line is 12.21, blue line is 90