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Question 1138238: Can someone please help? I’m completely confused on how to solve the equation:
Find the exponential function that passes through the points.
x: 1, 2, 3, 4
h(x): 40, 16, 6.4, 2.56
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! here's what i get.
general form for exponential function is y = ab^x.
when x = 1, you get ab^1 = 40
when x = 2, you get ab^2 = 16
when x = 3, you get ab^3 = 6.4
when x = 4, you get ab^4 = 2.56
if you take ab^2 and divide it by ab^1, you get .4
if you take ab^3 and divide it by ab^2, you get .4
if you take ab^4 and divide it by ab^3, you get .4
take a look at any one of these and you'll see that a drops out of the equation each time.
for example:
ab^4 / ab^3 = 2.56 / 6.4 = .4
this results in ab^4 / ab^3 = .4
the a in the numerator and the a in the denominator cancel out and you are left with b^4 / b^3 = .4
since b^4 / b^3 is equal to b^(4-3), you are left with b = .4
therefore, your equations become:
a * .4^1 = 40
a * .4^2 = 16
a * .4^3 = 6.4
a * .4^4 = 2.56
simplify to get:
a * .4 = 40 which means a = 100.
a * .4^2 = 16 becomes a * .16 = 16 which means a = 100
go down the line and a will be 100 each time.
your exponential equation in the form of ab^x becomes 100 * .4^x.
you can graph this function as shown below.
the graph shows that the solution is correct.
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