1. ## Growth function

Hi guys,

D = D010kt, where D is the diameter (in cm) of a tree t years after the beginning of a certain growth period. If the diameters after 2 and 5 years are 61.05cm and 82.45cm respectively, what is D0 and k.

Thanks in advance for help guys.

2. ## Re: Growth function

Take logs of the equation then subsitute the data given into the resulting equation and you will have a pair of simultaneous linear equations in $\log(D_0)$ and $k$ which you can then solve

Alternativly substitue the data into the original equation then divide one of the resulting equations by the other to get:

$\frac{D_2}{D_{5}}=10^{k(2-5)}$

which you can solve for $k$ and then go back to one of the original equations to solve for $D_0$

3. ## Re: Growth function

Originally Posted by zzephod
Take logs of the equation then subsitute the data given into the resulting equation and you will have a pair of simultaneous linear equations in $\log(D_0)$ and $k$ which you can then solve

Alternativly substitue the data into the original equation then divide one of the resulting equations by the other to get:

$\frac{D_2}{D_{5}}=10^{k(2-5)}$

which you can solve for $k$ and then go back to one of the original equations to solve for $D_0$

Did you mean to say D5/D2=10 ^3k

4. ## Re: Growth function

Originally Posted by bjhopper
Did you mean to say D5/D2=10 ^3k
Is that different from what I did say?

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5. ## Re: Growth function

Originally Posted by zzephod
Is that different from what I did say?

.
the decay factor= the growth factor but I am sure you are confusing the OP

6. ## Re: Growth function

The problem was to solve for k. Whether you do that by writing $\frac{D_5}{D_2}= \frac{82.45}{61.05}= \frac{D_0 10^{5k}}{D_0 10^{2k}}= 10^{3k}$ or $\frac{D_2}{D_5}= \frac{61.05}{82.45}= \frac{D_0 10^{2k}}{D_0 10^{5k}}= 10^{-3k}$ is irrelevant and I don't see why either would be more confusing than the other.
61.05cm and 82.45cm

7. ## Re: Growth function

a growth factor for tree diameter growth is given.Why would that equation be modified to a decay factor equation? Cosby is the one who should reply.

8. ## Re: Growth function

There is no "decay factor equation". Who is "Cosby"? I don't know what you are talking about.

9. ## Re: Growth function

Cosby is theOP.zzephod describes a decay equation and I am asking why.I said by showing one confuses the OP

10. ## Re: Growth function

Originally Posted by bjhopper
Cosby is theOP.zzephod describes a decay equation and I am asking why.I said by showing one confuses the OP
I do not describe a decay (or growth equation), that is your interpretation, but give a hint on how to find k from the original problem.

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11. ## Re: Growth function

Originally Posted by bjhopper
Cosby is theOP.zzephod describes a decay equation and I am asking why.I said by showing one confuses the OP
First, the OP is NOT "Cosby", he is "Coshy". Second the equation zzephod gives can be either "decay" or "growth" depending on the sign of k, which is to be determined.