b The general form of an exponential function is written as y=ab^x.
A
a y=0.4(0.5)^x
B
b y=8(2)^x
Practice makes perfect
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]
[-0.8em]
( 3, 0.05) & 0.05=ab^3 [0.4em]
[-0.8em]
( 5, 0.0125) & 0.0125=ab^5 [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.
|c|c|
[-0.8em]
Point & y=ab^x [0.4em]
[-0.8em]
( 1, 16) & 16=ab^1 [0.4em]
[-0.8em]
( 4, 128) & 128=ab^4 [0.4em]
If we combine these, we get a system of equations which can be solved by using the Substitution Method.
