Investigating Growth Patterns

[MathStudent21]

Hello,

I've got a graph here and I'm not quite sure to whether or not it is an exponential growth pattern.. It looks to be linear, however the assignment given it based on exponentials :S

We were provided with a table that goes as follows

Time (t) (Hours) 1 2.5 5 7 12 15 18
Population (PHI) (Millions) 18 20 23 27 37 46 56

From the data given I have been able to obtain Ln(Population) and goes as follows:

Natural Logarithm
(Population) 2.89 - 3 - 3.13 - 3.3 - 3.61 - 3.83 - 4.03
Dashes to show gaps between the data ^



This is the graph of ln(PHI) verses time and the question asks to investigate whether it is an exponential growth pattern.

I'm not sure how to explain or give reasons to why this is an exponential growth pattern =/

Furthermore, we are asked to calculate the gradient and y-intercept of the line of best fit for the graph, if anyone can lead me in the right direction please, it will be much appreciated

I will appreciate any help and thanks ALOT in advance will appreciate any help and thanks ALOT in advance

 

[tkhunny]

You've ln(PHI) = ax+b

What happens through anti-log? \(\displaystyle e^{ln(PHI)} = e^{ax+b}\)?

Simplify and what do you get?

 

[MathStudent21]

Through anti-logs of Ln Population you get back to Population (PHI) which is the growth pattern I think =/

 

[tkhunny]

Did you do the arithmetic?

Left-hand side ==> PHI
Right-hand side ==> What?

What do you conclude?

 

[MathStudent21]

Not too sure what you mean by that :S

 

[tkhunny]

I mean that you need to show ANY work at all. You do have a lovely graph, but does it mean anything to you?

You recognize a linear equation: y = mx+b, for example.

If your tripped over an exponential, would you recognize it?

Work out that right-hand side and see what you find.