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

question 153

Multiple Choice

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) \(0.07 t ^ { 3 } - 2.9 t ^ { 2 } - 0.79 t + 24.1\)

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Definitions:

Explanatory Power

The ability of a statistical model to account for the variance in a given data set, explaining how well the model fits or predicts the outcomes.

Security Returns

The gains or losses from investing in a financial security, calculated based on the change in investment value and any income from the investment, like dividends.

Systematic Factors

Factors that affect the entire market or a large segment of the market, such as economic, political, or social changes.

Expected Inflation

The anticipated rate at which the general level of prices for goods and services will rise over a period, eroding purchasing power.