a The general form of an exponential function is written as y=ab^x.
B
b Substituting the point (0,12) in the function, we can solve for the initial value.
A
a y=1/4(6)^x
B
b y=12(3/10)^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]
( 2, 9) & 9=ab^2 [0.4em]
[-0.8em]
( 4, 324) & 324=ab^4 [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 two points through which the exponential function passes. Notice though that one point is on the y-axis, (0,12). If we substitute this point into the general form of the exponential function, we can solve for a since a base raised to the zeroth power equals 1.
12=ab^0 ⇔ a=12When we know that a=12, we can find b by substituting the second point into the function and solving for b.
