Fill in the Blank : Each correct answer earns 1 point.

Escherichia Coli is common bacteria. The time (in minutes) and the number of bacterial cells in a culture have been recorded at five different moments. The first coordinate is the time and the second coordinate is the cell count. Using these observations, fill in the cells of the following table and estimate both the log-linear regression model and the corresponding exponential growth model.

• (0, 28)
• (15, 48)
• (30, 41)
• (45, 89)
• (60, 148)

Assume the time observations are represented by xi, and the cell count observations are represented by yi.

Individual(i)	xi	xix	(xix)2	log(yi)	log(yi)log(y)	(log(yi)log(y))2	(xix)(log(yi)log(y))
1	0			1.45
2	15			1.68
3	30			1.61
4	45			1.95
5	60			2.17
Total		---			---

• Calculate the mean time.

x =

• Calculate the time variance.

sx2 =

• Calculate the standard deviation of the time.

sx =

• Calculate the mean log cell count.

log(y) =

• Calculate the log cell count variance.

slog(y)2 =

• Calculate the standard deviation of the log cell count.

slog(y) =

• Calculate the covariance between the time and the log cell count.

COV(x,log(y)) =

• Calculate the correlation between the time and the log cell count observations.

r =

• Calculate the slope of the log-linear regression model.

B =

• Calculate the log y-intercept of the log-linear regression model.

A =

• Write the log-linear model.

log(y^(x)) =

• Calculate the factor a for the exponential model.

a =

• Calculate the base b for the exponential model.

b =

• Write the exponential model.

y^(x) =