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.
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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