# Thread: Power/Exponential Function - Weight of Chicken Embryo Over Time

1. ## Power/Exponential Function - Weight of Chicken Embryo Over Time

Directly from my math log.

• A power function has the form $\displaystyle y=ax^b$ where $\displaystyle a$ and $\displaystyle b$ are constants.
• You can use an exponential function to model a set of data pairs $\displaystyle (x,y)$ if there is a linear relationship between $\displaystyle x$ and $\displaystyle \log y$.
• You can use a power function to model a set of data pairs $\displaystyle (x,y)$ if there is a linear relationship between $\displaystyle \log x$ and $\displaystyle \log y$.
The table shows how the weight of a chicken embryo inside and egg changes over time.

1. Make a scatter plot, on your own graph paper, of the data pairs $\displaystyle (\log d, \log W)$. What relationship exists between $\displaystyle \log x$ and $\displaystyle \log W$?
2. Find an equation giving $\displaystyle W$ as a function of $\displaystyle d$.
3. A chick hatches 21 days after the egg is laid. Estimate the weight of a chick when it hatches.
All right I know the problem is long but I have done some of the work. I just need you guys to check if I did it right or not.
1. I graphed the data on graph paper and in my calculator based on $\displaystyle (\log d, \log W)$. It looks like the relationship between the coordinates is a linear relationship. Would that be right answer?
2. I found the equation by using linear regression on my calculator after I plotted my points of $\displaystyle (\log d, \log W)$. I got $\displaystyle W(d) = 4.043x - 3.688$ as the equation. But I also plot the graph based on $\displaystyle (d,W)$ and I found the power regression of the data which came out to be $\displaystyle W(d) = .00020502(d)^{4.043}$ and fit the data almost precisely. So which equation should I put as the answer?
3. For this I got 45.476 g, when $\displaystyle d=21$ based on the equation $\displaystyle W(d) = .00020502(d)^{4.043}$ and it seems reasonable. But when using $\displaystyle W(d) = 4.043x - 3.688$, I got 81.212 g.
Some of the questions asked a kind of vague to me so I don't really understand what it's asking. Help of any kind would be appreciated.

BTW - The table is attached to the thread.

2. Help anyone?