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20 May 2011, 09:08
Kudos
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Hi Guys,
I came across the below question in an online tutorial.
The average lifespan of American women has been tracked, and the model for the data is y = 0.2t + 73, where t = 0 corresponds to 1960. Explain the meaning of the slope and y-intercept.
They have used the linear equation concept in the problem (slope intercept form).
I had a question if exponential growth concept can be applied for the same problem? Because the growth is the fixed or same (0.2 every year) at regular interval(every year)
y=a(1+r)^t, where a = initial amount before measuring growth/decay
r = growth/decay rate (often a percent)
t = number of time intervals that have passed
y = exponential growth
using slope intercept form :y = 0.2t + 73
m = 0.2 this implies y increases by 0.2 (a constant amount) for every increase in 1 unit for 't' value.
for 1960 y = 0.2*0 + 73 = 73 , where t = 0 corresponds to starting year 1960
for 1961 it would be y = .2*1+73 = 73.04
aplying exponential growth formula for year 1960 i.e t=0 is
y = 73 (1+.2)^0 = 73
for year 1961 i.e t = 1,
y = 73 (1+.2)^1
y = 73* 1.2 = 87.6
we get differnet values for t = 1
Is the concept of exponential growth applicable to this problem?
Regards,
Anu
I came across the below question in an online tutorial.
The average lifespan of American women has been tracked, and the model for the data is y = 0.2t + 73, where t = 0 corresponds to 1960. Explain the meaning of the slope and y-intercept.
They have used the linear equation concept in the problem (slope intercept form).
I had a question if exponential growth concept can be applied for the same problem? Because the growth is the fixed or same (0.2 every year) at regular interval(every year)
y=a(1+r)^t, where a = initial amount before measuring growth/decay
r = growth/decay rate (often a percent)
t = number of time intervals that have passed
y = exponential growth
using slope intercept form :y = 0.2t + 73
m = 0.2 this implies y increases by 0.2 (a constant amount) for every increase in 1 unit for 't' value.
for 1960 y = 0.2*0 + 73 = 73 , where t = 0 corresponds to starting year 1960
for 1961 it would be y = .2*1+73 = 73.04
aplying exponential growth formula for year 1960 i.e t=0 is
y = 73 (1+.2)^0 = 73
for year 1961 i.e t = 1,
y = 73 (1+.2)^1
y = 73* 1.2 = 87.6
we get differnet values for t = 1
Is the concept of exponential growth applicable to this problem?
Regards,
Anu
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
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21 May 2011, 11:51
Kudos
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anuu
The average age has a linear relation with time, not exponential.
Every year, the average age increases by 0.2 (i.e. 0.2 is added to previous year's age).
When you try to use 73(1 + 0.2)^t, you are increasing 73 by 20% every year. (0.2 = 20%) That is not the given relation. Every year, the average age has to increase by 0.2 years, not 20%.
23 May 2011, 03:00
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Yes , the value could be 0.2 in the first instance but increasing it by 20% later is not same.
Mukesh
Mukesh
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
