Question

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?

Answer 1

Please see below.

Explanation:

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]}