Chapter 9.6, Problem 55E

(a)

To determine

To calculate: The instantaneous rate of change of the GDP in 2005 and 2015 and interpret it. The table shows U.S. gross domestic product (GDP) in billions of dollars for selected years from 2000 to 2070. Assume that the GDP can be modeled with the function $G\left(t\right)=212.9{\left(0.2t+5\right)}^3-5016{\left(0.2t+5\right)}^2+8810.4t+104,072$ where $G\left(t\right)$ is in billions of dollars and t is the number of years past 2000.

(b)

To determine

To calculate: The average rate of change of the GDP from 2005 to 2015 using the data given. The table shows U.S. gross domestic product (GDP) in billions of dollars for selected years from 2000 to 2070. Assume that the GDP can be modeled with the function $G\left(t\right)=212.9{\left(0.2t+5\right)}^3-5016{\left(0.2t+5\right)}^2+8810.4t+104,072$ where $G\left(t\right)$ is in billions of dollars and t is the number of years past 2000.

(c)

To determine

The wellness of average rate of change of the GDP from 2005 to 2015 approximates the instantaneous rate of change of GDP in 2020. The table shows U.S. gross domestic product (GDP) in billions of dollars for selected years from 2000 to 2070. Assume that the GDP can be modeled with the function $G\left(t\right)=212.9{\left(0.2t+5\right)}^3-5016{\left(0.2t+5\right)}^2+8810.4t+104,072$ where $G\left(t\right)$ is in billions of dollars and t is the number of years past 2000.