SOLUTION: Write an exponential function of the form y=ab^x whose graph passes through the given points. 17. (1,4),(2,12)

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Write an exponential function of the form y=ab^x whose graph passes through the given points. 17. (1,4),(2,12)      Log On


   

Question 72913This question is from textbook mcgougal littell algebra 2
: Write an exponential function of the form y=ab^x whose graph passes through the given points.
17. (1,4),(2,12) This question is from textbook mcgougal littell algebra 2

Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Plug in both x and y into the general form
y=ab%5Ex
4=ab%5E1Plug in (1,4)
b=4%2Fasolve for b
12=ab%5E2Plug in point (2,12)
Now plug in b=4/a into b of 12=ab%5E2
12=a%284%2Fa%29%5E2
12=a%2816%2Fa%5E2%29
12=16%2FaSolve for a
a=16%2F12
a=4%2F3Plug this into y=ab%5Ex with any point also
4=%284%2F3%29b%5E1Solve for b
4%283%2F4%29=b
b=3
So the equation is
y=%284%2F3%29%283%29%5Ex
Check:
Plug in x=1, you should get y=4
y=%284%2F3%29%283%29%5E1
y=4works


Plug in x=2, you should get y=12
y=%284%2F3%29%283%29%5E2
y=%284%2A9%29%2F3
y=12works


Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Write an exponential function of the form y=ab^x whose graph passes through the given points.
(1,4),(2,12)
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The form is y = ab^x
12 = ab^2
4 = ab^1
------------
Divide the 1st by the 2nd to get:
3 = b
--------
Substitute that into the 2nd equation to solve for "a":
4 = a*3^1
a=(4/3)
-------------
EQUATION:
y = (4/3)*2^x
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Cheers,
Stan H.