Plot the following points on a rectilinear grid add a

Question

• Plot the following points on a rectilinear grid. Add a linear trendline with the equation and R² value. Re-plot the graph on a semilog grid to determine if an exponential equation (y = be^mx) is a good representation of the data. Add a trendline with the equation and R² value. Do you think an exponential equation is appropriate for this data set? Why or why not? Save this problem on a worksheet named "problem 1".

x	y
0.00	1.80
0.20	3.60
0.40	7.30
0.60	14.70
0.80	29.60
1.00	59.60

• The rate of water (Q) discharging through an orifice of diameter 2.5 cm is a function of the pressure head H. Plot the following empirical data points on a rectilinear grid. Add a linear trendline with the equation and R² value. Re-plot the graph on a log-log grid to determine if a power equation (y = b * x^m) is a good representation of the data. Add a trendline with the equation and R² value. Do you think power equation is appropriate for this data set? Why or why not? Save this problem on a worksheet named "problem 2".

Q (m3/s) H (m) 0.11 0.35 0.14 0.53 0.17 0.76 0.20 1.04 0.28 1.37 0.26 1.68 0.28 2.10 0.43 4.72 0.57 8.23 0.71 13.11 0.85 19.20

• Biosystems engineers often need to understand how plant diseases spread in order to formulate effective control strategies.

Grey leaf spot of corn is a disease that shows up as lesions and can reduce photosynthesis and yield. In extreme cases it can result in loss of the entire crop.

To study the disease, observations were taken of the number of lesions per leaf during the growing season. At the start of the study, which we call day 0, there was 1 lesion per 20 leaves, or 0.05 per leaf. The entire results of the observations are shown below.

Day	Lesions per Leaf
0	0.05
20	0.1
30	0.2
40	0.26
60	0.6
80	1.3
90	2
110	4
120	6
140	17
150	20
170	40
190	112
200	151

• Show the resulting data and trendline, with equation and R2 value, on the appropriate graph type (rectilinear, semilog or log-log) to make the data appear linear.
• According to the model, how many lesions were there at day 97?
• If the model continued to be accurate, how many days would be required to reach 250 lesions per leaf?