## Precalculus (6th Edition) Blitzer

a. $5.8\sqrt {10}$ million. b. $18.3$ million; underestimates by 5.8 million.
a. Given the formula $E=5.8\sqrt x+56.4$, at year 2030, we have $x=2030-2020=10$ and $E_1=5.8\sqrt {10}+56.4$. At year 2060, we have $x=2060-2020=40$ and $E_2=5.8\sqrt {40}+56.4=11.6\sqrt {10}+56.4$. Thus the projected increase is $\Delta E=E_2-E_1=5.8\sqrt {10}$ millions. b. The above result can be approximated to $\Delta E\approx18.3$ million. Reading from the bar graph, we have the difference as $\Delta E_0=98.2-74.1=24.1$ million. We have $24.1-18.3=5.8$; thus the model underestimates the difference from the bar graph by about 5.8 million.