Solve the Problem $f ( t ) = 0.05 t ^ { 3 } - 0.6 t ^ { 2 } + 1.25 t + 2.5$

Multiple Choice

Solve the problem.
-A company models its yearly expenses in millions of dollars using the equation $f ( t ) = 0.05 t ^ { 3 } - 0.6 t ^ { 2 } + 1.25 t + 2.5$ where $t = 0$ represents 1986 . The company's account manager decides to adjust the model so that $t = 0$ corresponds to 1991 rather than 1986 . To do this, she obtains $g ( t ) = f ( t + 5 )$ . Use the Binomial Theorem to express $g ( t )$ in descending powers of $t$ .

A) $0.05 \mathrm { t } ^ { 3 } + 0.15 \mathrm { t } ^ { 2 } - 1 \mathrm { t } + 0$
B) $0.05 \mathrm { t } ^ { 3 } - 1.35 \mathrm { t } ^ { 2 } + 11 \mathrm { t } + 2$
C) $0.05 t ^ { 3 } + 0.15 t ^ { 2 } + 11 t + 6$
D) $0.05 t ^ { 3 } - 1.35 t ^ { 2 } - 2.25 t + 12$ 3 Find a Particular Term in a Binomial Expansion
Write the first three terms in the binomial expansion, expressing the result in simplified form.