1)
I think you should start off by solving the function equal to the given growth.
[tex]f(m) = 5.98[/tex]
[tex]3(1.09) {}^{m} = 5.98[/tex]
[tex]1.09 {}^{m} = \frac{5.98}{3} [/tex]
[tex]1.09 {}^{m} = 1.9933[/tex]
[tex]m \times ln(1.09) = ln(1.9933) [/tex]
[tex]m = \frac{ ln(1.9933) }{ ln(1.09) } = 8 [/tex]
It is sufficient to plot the exponential growth over the domain m [0,8]
2)
The y-intercept in this case represents the growth achieved at the beginning when m=0.
Before the experiment started::
3)
I'm not really sure about this one,but i think it's supposed to be solved according to this eq,,
[tex]c = \frac{f(8) - f(2)}{8 - 2} [/tex]
Note that c is the average rate of change.
Find f(2) first by substituting 2 in f(m)
f(2)=3(1.09)²=3.5643
[tex]c = \frac{5.98 - 3.5643}{ 8 - 2} [/tex]
[tex]c = \frac{2.4157}{6} = 0.4026[/tex]
average growth=0.4026 cm/month
