Function Of Time In Math

By Author: Stevan Crasta
Total Articles: 2
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Introduction to function of time in math:

In this article we shall discuss about functional variation with time. We will work out a few word problems based on function of time. An exponential function is an example of function of time. General form of an exponential function is given by y=f(t)=k e^t , where k-constant, variable t-time, variable e-base.Here the function f(t) is time dependent.

Worked Example - Function of Time in Math

Exponential function growth- Function of time in math

Exponential function growth is defined as `y=h (p)^t`

where,

h-Number at initial

p-growth factor (calculated as follow)

(p=1+r,here r is given growth percentage)

t-time

Example problem-1

A bunch of cherry fruits of 200 house fly increase by 5% in an hour. How many house fly will be in the cherry fruit after

1 hour?

Given:

h=200

p=1+r=1+0.05=1.05

t=1 hour

Solution:

Exponential function ` y=h (p)^t`

Substitute the given data in the formulae

`y=200(1.05)^1`

y=200(1.05)

y=210

y=210 house ...
... fly

Example problem-2

John borrows a amount of $10,000 from a money lender with an interest of 5% compounded annually. How much should he pay as interest to the money lender after 2 years?

Given:

h=10,000

p=1+r=1+0.05=1.05

t=2 year

Solution:

Exponential function ` y=h (p)^t`

Substitute the given data in the formulae

`y=10,000(1.05)^2`

y=10,000(1.1025)

y=11,025

Total amount =$11,025

Interest=11,025-10,000=$1,025

Example problem-3

Calculate how long a single WBC-cell will take to produce 20,000 WBC-cell?

Solution:

Assume this function to solve exponential function word problem based on population.

`f(t)=2^t`

`20,000=2^t`

Calculate the natural logarithm on both side

`ln(20,000)=ln(2^t)`

ln(20,000)= t ln(2)

`t= ln(20,000)/ ln(2)`

`t=(9.9)/0.693=14.29`

After 14.29 min the WBC-cell can produce 20,000 WBC-cells

Exponential Function Decay- Function of Time in Math

Exponential function growth is defined as `y=h (p)^t`

where,

h-Number at initial

p-growth factor (calculated as follow)

(p=1-r,here r is given growth percentage)

t-time

Example problem-4

A bunch of cherry fruits of 200 house fly decrease by 10% in an hour. How many house fly will be in the cherry fruit after 1 hour?

Given:

h=200

p=1-r=1-0.1=0.9

t=1 hour

Solution:

Exponential function ` y=h (p)^t`

Substitute the given data in the formulae

`y=200(0.9)^1`

y=200(0.9)

y=180

y=180 house fly

Example problem-5

The price of a coffee-maker is $7,000 which decreases at a rate of interest of 10%.What is the price of a coffee-maker after 1 year?

Given:

h=7,000

p=1-r=1-0.1=0.9

t=1 year

Solution:

Exponential function ` y=h (p)^t`

Substitute the given data in the formulae

`y=7,000(0.9)^1`

y=7,000(0.9)

y=6,300

The price of a coffee-maker after 1 year=$6,300

These are the some example problem for function of time in math.

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