Points (1,18) and (4,3888) must satisfy the given equation.
B
b
Points (-2,-8) and (3,-0.25) must satisfy the given equation.
A
a
y=3*6^x
B
b
y=-2(0.5)^x
Practice makes perfect
a
We want to write an exponential function for the graph that passes through the points (1,18) and (4,3888). Let's consider the general form for this type of function.
y=ab^x
Since we want the points to lie on the graph, they must satisfy this equation. Let's substitute (1,18) into the above formula.
We received two equations, so to find the values of a and b we need to solve the system of equations.
ab=18 & (I) ab^3=3888 & (II)
The first equation says that the product of a and b is 18. Notice that the second equation contains the same expression multiplied by b^3.
ab=18 ab^4=3888 ⇒ ab=18 ab* b^3=3888
This allows us to substitute the value of ab into the second equation and solve for b.
Now we need to solve the system of equations that we found.
a/b^2=-8 & (I) ab^3=- 14 & (II)
To solve it we can use the Substitution Method. Let's multiply both sides of the first equation by b^2 to isolate a.
a/b^2=-8 ab^3=- 14 ⇒ a=-8 b^2 ab^3=- 14
This allows us to substitute the value of a into the second equation and solve for b.
