The time (in years) and mass (in micrograms) of 5 observations of radioactive hydrogen (tritium) are recorded in the following list of data. The first coordinate is the time and the second coordinate is the mass. Using these observations, fill in the cells of the following table and estimate both the log-linear regression model and the corresponding exponential decay model.

• (0, 128.82)
• (15, 46.77)
• (30, 15.49)
• (45, 16.22)
• (60, 4.79)

Assume the time observations are represented byxi, and the mass observations are represented byyi.

A Table of Intermediate Calculations for the Time and Log Mass Standard Deviations and Correlation
Individual(i)	xi	xix	(xix)2	log(yi)	log(yi)log(y)	(log(yi)log(y))2	(xix)(log(yi)log(y))
1	0			2.11
2	15			1.67
3	30			1.19
4	45			1.21
5	60			0.68
Total		---			---

• Calculate the mean time.

x=

• Calculate the time variance.

sx2=

• Calculate the standard deviation of the time.

sx=

• Calculate the mean log mass.

log(y)=

• Calculate the log mass variance.

slog(y)^2=

• Calculate the standard deviation of the log mass.

slog(y)=

• Calculate the covariance between the time and the log mass.

COV(x,log(y))=

• Calculate the correlation between the time and the log mass observations.

r=

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

B=

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

A=

• Write the log-linear model.

log(y^(x))=

• Calculate the factorafor the exponential model.

a=

• Calculate the basebfor the exponential model.

b=

• Write the exponential model.

y^(x)=