SOLUTION: 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.

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.

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
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

ab = 10
a = 10/b
:
x=6.5, y=90

replace a with 10/b
*
10*
divide both sides by 10

using natural logs
5.5*ln(b) = ln(9)
ln(b) =
using your calc
ln(b) = .3995
b = 1.491
find a
a = 10/1.491
a = 6.707
the equation
f(x) =
:
"find the value of f(1.5), to the nearest hundred.
f(x) =
using your calc
f(1.5) = 12.21
:
looks like this

green line is 12.21, blue line is 90
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