Write an exponential function

You can write an exponential function from two points on the function's graph. For example, write an exponential function y = abx for a graph that includes (1,1) and (2, 4)

Use the general form of the exponential function y = abx and substitute for x and y using (1, 1)

1 = ab1

1 = ab

Divide both sides by b to solve for a

a  =  
1 / b

Use the general form of the exponential function y = abx again and substitute for x and y using (2, 4)

4 = ab2

Substitute    
1 / b
   for a in 4 = ab2

4   =  
1 / b
b2

4   =  
b2 / b


4 = b.

a  =  
1 / b

a  =  
1 / 4

The exponential function is y = (1/4)(4)x


Example #2

Find y = abx for a graph that includes (1,-2) and (2, -1)

Use the general form of the exponential function y = abx and substitute for x and y using (1, -2)

-2 = ab1

-2 = ab

Divide both sides by b to solve for a

a  =  
-2 / b

Use the general form of the exponential function y = abx again and substitute for x and y using (2, -1)

-1 = ab2

Substitute    
-2 / b
   for a in -1 = ab2

-1   =  
-2 / b
b2

-1   =  
2b2 / b

-1 = -2b

1  = 2b

b   =  
1 / 2

a   =  
-2 / b

a   =  
-2 / 1/2
= -2 × 2 = -4

The exponential function is y = -4(1/2)x

Recent Articles

  1. Probability Line - Definition and Examples

    Nov 21, 19 02:38 PM

    What is a probability line ? Things that you must know before doing problems ...

    Read More

New math lessons

Your email is safe with us. We will only use it to inform you about new math lessons.

                                 Follow me on Pinterest

Real Life Math Skills

Learn about investing money, budgeting your money, paying taxes, mortgage loans, and even the math involved in playing baseball.