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)

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 = abx with the values we found.

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

A more complicated example showing how to write an exponential function.

Example #2

Find y = abx for a graph that includes (1, 2) and (-1, 8)

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 (-1, 8)

8 = ab-1

Substitute
2 / b
for a in 8 = ab-1

8   =
2 / b
b-1

Multiply both sides of the equation by b2.

b2 × 8   =
2 / b
b-1 × b2

b2 × 8   =
2 / b
b

b2 × 8 = 2

Divide both sides of the equation by 8

(b2 × 8) / 8 = 2 / 8

b2 = 2 / 8

b2 = 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

Recent Articles

1. What is Statistics? Definition and Examples

Aug 16, 22 04:10 AM

What is statistics? The word statistics can mean two different things. First, it may refer to numerical facts ...

Check out some of our top basic mathematics lessons.

Formula for percentage

Math skills assessment

Compatible numbers

Surface area of ​​a cube