The u S population in 1910 was 92 million people. In 1990 the population was 250 million. How do you use the information to create both a linear and an exponential model of the population?

The linear model means that there is a uniform increase and in this case of US population from #92# million people in #1910# to #250# million people in #1990#.

This means an increase of #250-92=158# million in #1990-1910=80# years or

#158/80=1.975# million per year and in #x# years it will become

#92+1.975x# million people. This can be graphed using the linear function #1.975(x-1910)+92#,
graph{1.975(x-1910)+92 [1890, 2000, 85, 260]}

The exponential model means that there is a uniform proportional increase i.e. say #p%# every year and in this case of US population from #92# million people in #1910# to #250# million people in #1990#.

This means an increase of #250-92=158# million in #1990-1910=80# years or

#p%# given by #92(1+p)^80=250# which gives us #(1+p)^80=250/92# which simplifies to #p=(250/92)^0.0125-1=0.0125743# or #1.25743%#.

This can be graphed as an exponential function #92xx1.0125743^((x-1910))#, which gives population in a year #y# and this appears as
graph{92(1.0125743^(x-1910)) [1900, 2000, 85, 260]}