SOLUTION: Find the equation for an exponential function that passes through the pair of points given below. (Round all coefficients to four decimal places when necessary.) through (−1,

Algebra ->  Exponents -> SOLUTION: Find the equation for an exponential function that passes through the pair of points given below. (Round all coefficients to four decimal places when necessary.) through (−1,       Log On


   

Question 1197442: Find the equation for an exponential function that passes through the pair of points given below. (Round all coefficients to four decimal places when necessary.)
through
(−1, −4) and (2, −0.5)
Found 3 solutions by josgarithmetic, MathLover1, greenestamps:
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
y=a*b^x

ab%5Ex=y

first point
a%2Ab%5E%28-1%29=-4
a%2Fb=-4
b%2Fa=-1%2F4
a=-4%2Fb

second point
ab%5E2=-0.5
%28-4%2Fb%29b%5E2=-0.5
%284%2Fb%29b%5E2=0.5
4b=0.5
b=0.5%2F4
b=5%2F40
highlight_green%28b=1%2F8%29
.
.

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

Find the equation for an exponential function that passes through the pair of points given below. (Round all coefficients to four decimal places when necessary.)

An exponential function is defined by the formula
f%28x%29+=+a%2Ab%5Ex
if passes through (-1, -4) , we have
-4+=+a%2Ab%5E-1
-4+=+a%2A1%2Fb
a=+-4+b..........eq.1
and (2, -0.5), we have
-0.5+=+a%2Ab%5E2
a=-%281%2F2%29%2Fb%5E2
a=-1%2F%282b%5E2%29............eq.2

+-4+b=-1%2F%282b%5E2%29.
+-4+b%2A2b%5E2+=-1
+-8b%5E3+=-1
+b%5E3+=-1%2F-8
+b+=root%283%2C1%2F8%29
b=1%2F2

then
a=+-4+%281%2F2%29..........eq.1
a=+-2
your equation is:
f%28x%29+=+-2%2A%281%2F2%29%5Ex



Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


y = ab^x

The two given points give us

(1) -4=ab%5E%28-1%29
(2) -0.5=ab%5E2

Divide (2) by (1) to get

b%5E3=1%2F8
b=1%2F2

Use that value in either (1) or (2) to find a.

-4=a%281%2F2%29%5E%28-1%29=2a
a=-2

ANSWER: y=ab%5Ex=%28-2%29%281%2F2%29%5Ex