Given:
Graph of
A. observed rates of population growth in five-year intervals between 1990 and 2010
B. The linear empirical formula that models the data in (A) above, given as
r(t)=-0.07t+1.06 ............................(1)
where
r=population growth rate in percent
t=number of years after 1990.
#20
All answers refer to predicted population increases, which relates to the dependent variable r(t) (as opposed to the "coefficient t" as indicated in the question). It will be assumed that the interpretation of r(t) was intended, in which case it is the predicted annual population decrease rate (-0.07) in percent, which is the slope of equation (1) above. The rate is interpreted as -0.07% every single year. The five year period refers only to the observed data (shown as dots in the graph).
#21
The year 1990+t which has a population rate y(t)=-1 can be found by solving equation (1), giving y(t)=-1. =>
-1=1.06-0.07t ....................(1a)
Solve for t
t=(1.06+1)/0.07=29.42
The exact year is 1990+t=1990+29.42=2019.42.
This will have to be rounded up to match one of the provided answers.