Chapter 4, Problem 58RE

(a)

To determine

To calculate: The rate of increase of sea level in $2000$ $\left(t=100\right)$ if the cubic curve that Marjory Duffin obtained after purchasing a beachfront condominium in New York using regression is $L\left(t\right)=-0.0001t^3+0.02t^2+2.2t$ mm where t is a time in years since $1990$. The graph shows the curve and related data.

(b)

To determine

To calculate: The rate of increase in sea level in $2025$ $\left(t=125\right)$ if the cubic curve that Marjory Duffin obtained after purchasing a beachfront condominium in New York using regression is $L\left(t\right)=-0.0001t^3+0.02t^2+2.2t$ mm where t is a time in years since $1990$. The graph shows the curve and related data.

(c)

To determine

To graph: The sketch of the function L for $\left(0\le t\le 200\right)$ and determine whether sea level through $2100$ can be predicted using the function where the cubic curve that Marjory Duffin obtained after purchasing a beachfront condominium in New York using regression is $L\left(t\right)=-0.0001t^3+0.02t^2+2.2t$ mm where t is a time in years since $1990$. The graph shows the curve and related data.

(d)

To determine

The comments on the assertion according to James Stewart who is a summer intern at Duffin House publishers, that “the cubic curve comes from doing a regression on original data and therefore reflects the actual trend of the data and this is reality and cannot argue against reality”.