Chapter Closure
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The general form of an exponential function is written as y=ab^x.
The general form of an exponential function is written as y=ab^x.
y=11(3)^x
y=40(0.8)^x
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.
(II): a= 99/b^2
(II): a/c* b = a* b/c
(II): Calculate quotient
(II): .LHS /99.=.RHS /99.
(II): Rearrange equation
(II): sqrt(LHS)=sqrt(RHS)
(II): b > 0
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.
Now we can complete the equation. y=11(3)^x
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|
[-0.8em]
Point & y=ab^x [0.4em]
[-0.8em]
( -1, 50) & 50=ab^(-1) [0.4em]
[-0.8em]
( 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.
(I):LHS * b=RHS* b
(II): a= 50b
(II): Multiply
(II): .LHS /50.=.RHS /50.
(II): Rearrange equation
(II): sqrt(LHS)=sqrt(RHS)
To find a, we substitute the value of b back into the first equation and evaluate.
Now we can complete the equation. y=40(0.8)^x