Delayed Exponential Function Learning

Introduction of delayed exponential function learning:-

Delayed exponential function learning is the new way for the students. Student does learning the exponential delayed function definition and also solves the example problems. In math exponential decay function means decrease the rate of a value or delayed the rate of the value. It is modulated by a differential equation.

`(dN)/(dt) = -lambda N`

Where,

N – quantity

`lambda` – positive number

This is also called as decay constant.

Basic Formula for Delayed Exponential Function Learning:-

In the following basic formula for delayed exponential function learning

`N = N_o e^(kt) ` , where k<0 br="">
Where

N = population

`N_0` = initial population

k = delay rate

t = time

Example Problems for Delayed Exponential Function Learning:-

Problem 1:-

Solve the delayed exponential function relation `y=3^-x` and use approximate value of y

1.      -1.2
2.      -2.2
3.      -3.2

Solution:

Given: `y = 3^-x`

Put the value x = -1.2

`y = 3^(-x)`

= `3^(-(-1.2))`

= `3^(1.2)`

= 3.737

Put the value x = -2.2

`y = 3^(-x)`

= `3^(-(-2.2))`

= `3^(2.2)`

= 11.21

Put the value x = -3.2

`y = 3^(-x)`

= `3^(-(-3.2))`

= `3^(3.2)`

= 33.63

Here y values is decreased and x values is increased. So this type of function is called as delayed exponential function. I have recently faced lot of problem while learning basic math word problems, But thank to online resources of math which helped me to learn myself easily on net.

Problem 2:-

Solve the delayed exponential function relation `y = 2^-x. -4<=x<=4 `

Solution:

Find the ordered pairs to satisfy the equation.

Put the value x = -4

`y = 2^(-x)`

`= 2^(-(-4))`

`= 2^(4)`

= 16

Put the value x = -3

`y = 2^(-x)`

`= 2^(-(-3))`

` = 2^(3)`

= 8

Put the value x = -2

y = 2^(-x)

= 2^(-(-2))

= 2^(2)

= 4

Put the value x = -1

`y = 2^(-x)`

`= 2^(-(-1))`

` = 2^(1)`

= 2


Put the value x = 0

`y = 2^(-x)`

`= 2^(-0)`

= 1

Put the value x = 1

` y = 2^(-x)`

`= 2^(-(1))`

` = 2^(-1)`

= 0.5

Put the value x = 2

`y = 2^(-x)`

`= 2^(-(2))`

`= 2^(-2)`

= 0.3

Put the value x = 3

`y = 2^(-x)`

`= 2^(-(3))`

`= 2^(-3)`

= 0.1

Put the value x = 4

`y = 2^(-x)`

`= 2^(-(4))`

` = 2^(-4)`

= 0.0625

When x is 0, y is 1. So, the y–intercept is 1.

Here y values is decreased and x values is increased. So this type of function is called as delayed exponential function.