Expand a Binomial Raised to a Power
-A company models its yearly expenses in millions of dollars using the equation $f ( t ) = 0.07 t ^ { 3 } - 0.8 t ^ { 2 } + 1.21 t + 3.3$ where $t = 0$ represents 1988 . The company's account manager decides to adjust the model so that $t = 0$ corresponds to 1998 rather than 1988 . To do this, she obtains $g ( t ) = f ( t + 10 )$. Use the Binomial Theorem to express $g ( t )$ in descending powers of $t$.
A) $0.07 \mathrm { t } ^ { 3 } + 1.3 \mathrm { t } ^ { 2 } + 6.21 \mathrm { t } + 5.4$
B) $0.07 t ^ { 3 } - 2.9 t ^ { 2 } + 38.21 t + 3.51$
C) $0.07 \mathrm { t } ^ { 3 } + 1.3 \mathrm { t } ^ { 2 } + 38.21 \mathrm { t } + 8.1$
D) $0.07 t ^ { 3 } - 2.9 t ^ { 2 } - 0.79 t + 24.1$

Question

Quizplus · Accepted Answer

The correct answer is A because $g ( t ) = f ( t + 10 ) = 0.07 ( t + 10 ) ^ { 3 } - 0.8 ( t + 10 ) ^ { 2 } + 1.21 ( t + 10 ) + 3.3$$= 0.07 ( t ^ { 3 } + 30 t ^ { 2 } + 300 t + 1000 ) - 0.8 ( t ^ { 2 } + 20 t + 100 ) + 1.21 ( t + 10 ) + 3.3$$= 0.07 t ^ { 3 } + 2.1 t ^ { 2 } + 21 t + 70 - 0.8 t ^ { 2 } - 16 t - 80 + 1.21 t + 12.1 + 3.3$$= 0.07 t ^ { 3 } + 1.3 t ^ { 2 } + 6.21 t + 5.4$

Expand a Binomial Raised to a Power -A Company Models f(t)=0.07t3−0.8t2+1.21t+3.3f ( t ) = 0.07 t ^ { 3 } - 0.8 t ^ { 2 } + 1.21 t + 3.3f(t)=0.07t3−0.8t2+1.21t+3.3

Expand a Binomial Raised to a Power
-A Company Models $f ( t ) = 0.07 t ^ { 3 } - 0.8 t ^ { 2 } + 1.21 t + 3.3$