SOLUTION: Determine whether the table could represent a function that is linear, exponential, or neither. If it appears to be exponential, find a function that passes through the points. x:

Algebra ->  Exponents -> SOLUTION: Determine whether the table could represent a function that is linear, exponential, or neither. If it appears to be exponential, find a function that passes through the points. x:      Log On


   

Question 1177015: Determine whether the table could represent a function that is linear, exponential, or neither. If it appears to be exponential, find a function that passes through the points.
x: 1, 2, 3, 4
h(x): 70, 49, 34.3, 24.01
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

it appears to be exponential
to find an equation of the form use given points
(1,70),(2,49), plug in
f%28x%29=ab%5Ex%E2%80%8B%E2%80%8B
make a system of two equations, and then solve the system for a and+b
f%28x%29=ab%5Ex%E2%80%8B%E2%80%8B......use (1,70)
70=ab%5E1
ab=70...solve for a
a=70%2Fb....eq.1

f%28x%29=ab%5Ex%E2%80%8B%E2%80%8B......use (2,49)
49=ab%5E2
ab%5E2=49
a=49%2Fb%5E2....eq.2
from eq.1 and eq.2 we have
70%2Fb=49%2Fb%5E2...cancel one b
70%2F1=49%2Fb
b=49%2F70

find a
a=70%2Fb....eq.1
a=70%2F%2849%2F70%29
a=%2870%2A70%29%2F49
a=100
your equation is:
+f%28x%29=100%2A%2849%2F70%29%5Ex%E2%80%8B%E2%80%8B