You can write an exponential function from two points on the function's graph. For example, write an exponential function y = ab^{x} for a graph that includes (1,1) and (2, 4)
Use the general form of the exponential function y = ab^{x} and substitute for x and y using (1, 1)
1 = ab^{1}
1 = ab
Divide both sides by b to solve for a
Use the general form of the exponential function y = ab^{x} again and substitute for x and y using (2, 4)
4 = ab^{2}
4 = b.
The exponential function is y = (1/4)(4)^{x}
Example #2
Find y = ab^{x} for a graph that includes (1,-2) and (2, -1)
Use the general form of the exponential function y = ab^{x} and substitute for x and y using (1, -2)
-2 = ab^{1}
-2 = ab
Divide both sides by b to solve for a
Use the general form of the exponential function y = ab^{x} again and substitute for x and y using (2, -1)
-1 = ab^{2}
-1 = -2b
1 = 2b
The exponential function is y = -4(1/2)^{x}
Apr 20, 18 12:54 PM
Modeling exponential growth with the exponential function y = ab^x
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Apr 20, 18 12:54 PM
Modeling exponential growth with the exponential function y = ab^x
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