You can write an exponential function from two points on the function's graph. For example, write an exponential function y = ab^{x} for a graph that includes (1,1) and (2, 4)
The goal is to use the two given points to find a and b. Then, we can replace a and b in the equation y = ab^{x} with the values we found.
Use the general form of the exponential function y = ab^{x} and substitute for x and y using (1, 1)
1 = ab^{1}
1 = ab
Divide both sides by b to solve for a
Use the general form of the exponential function y = ab^{x} again and substitute for x and y using (2, 4)
4 = ab^{2}
4 = b.
The exponential function is y = (1/4)(4)^{x}
Example #2
Find y = ab^{x} for a graph that includes (1, 2) and (-1, 8)
Use the general form of the exponential function y = ab^{x} and substitute for x and y using (1, 2)
2 = ab^{1}
2 = ab
Divide both sides by b to solve for a
Use the general form of the exponential function y = ab^{x} again and substitute for x and y using (-1, 8)
8 = ab^{-1}
b^{2} × 8 = 2
Divide both sides of the equation by 8
(b^{2} × 8) / 8 = 2 / 8
b^{2} = 2 / 8
b^{2} = 1 / 4
b = square root of 1 / 4
b = 1 / 2
Now, let us find a using the equation a = 2 / b
a = 2 ÷ 1 / 2 = 2 / 1 ÷ 1 / 2 = 2 / 1 × 2 / 1 = 4 / 1 = 4
The exponential function is y = 4(1/2)^{x}
Jul 03, 20 09:51 AM
factoring trinomials (ax^2 + bx + c ) when a is equal to 1 is the goal of this lesson.
Basic math formulas
Algebra word problems
New math lessons
Your email is safe with us. We will only use it to inform you about new math lessons.