b The general form of an exponential function is written as y=ab^x.
A
a y=11(3)^x
B
b y=40(0.8)^x
a The general form of an exponential function is written in the following format.
y=ab^x
To find the equation, we need to determine a and b. From the exercise, we know that the function passes through two points. This means we can substitute both of these points in the function creating two equations.
|c|c|
[-0.8em]
Point & y=ab^x [0.4em]
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( 2, 99) & 99=ab^2 [0.4em]
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( 6, 8019) & 8019=ab^6 [0.4em]
If we combine these, we get a system of equations which we can be solved by using the Substitution Method.
Notice that b must be non-negative since we cannot have a negative base in an exponential function. To find a, we substitute the value of b back into the first equation and evaluate.
b Like in Part A, we have to substitute the known points into the general form of an exponential function and then solve for a and b.
|c|c|
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Point & y=ab^x [0.4em]
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( -1, 50) & 50=ab^(-1) [0.4em]
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( 2, 25.6) & 25.6=ab^2 [0.4em]
If we combine these, we get a system of equations which can be solved by using the Substitution Method.
