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.

Algebra ->  Exponential-and-logarithmic-functions -> 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.       Log On


   



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) About Me  (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
a%2Ab%5E1+=+10
ab = 10
a = 10/b
:
x=6.5, y=90
a%2Ab%5E6.5+=+90
replace a with 10/b
10%2Fb*b%5E6.5+=+90
10*b%5E5.5+=+90
divide both sides by 10
b%5E5.5+=+9
using natural logs
5.5*ln(b) = ln(9)
ln(b) = ln%289%29%2F5.5
using your calc
ln(b) = .3995
b = 1.491
find a
a = 10/1.491
a = 6.707
the equation
f(x) = 6.707%2A1.491%5Ex
:
"find the value of f(1.5), to the nearest hundred.
f(x) = 6.707%2A1.491%5E1.5
using your calc
f(1.5) = 12.21
:
looks like this
+graph%28+300%2C+200%2C+-4%2C+10%2C+-10%2C+100%2C+6.707%2A1.491%5Ex%2C+12.21%2C+90%29+
green line is 12.21, blue line is 90