Find a Power Function That Models the Data in the Table

question 216

Multiple Choice

Find a power function that models the data in the table. Round to three decimal places if necessary.
-The population of a small town is given by the table. $\begin{array}{r|rrrr}\text { Year } & 1980 & 1990 & 2000 & 2010 \\\hline \mathrm{P} & 7500 & 7513 & 7552 & 7617\end{array}$

If the population is modeled by $\mathrm { p } ( \mathrm { t } ) = \mathrm { at } ^ { 2 } + \mathrm { b }$ where $\mathrm { t }$ is in years and $\mathrm { t } = 0$ corresponds to the year 1980 and $t = 1$ corresponds the year 1990 , find $a$ .

• A) 26
• B) 30
• C) 15
• D) 13

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Definitions:

Perpetuity

A type of financial instrument that provides an infinite stream of interest payments.

Yield

The income return on an investment, such as the interest or dividends received, expressed as an annual percentage of the investment's cost or current market value.

Zero-coupon Bond

A bond that does not pay periodic interest and is sold at a discount to its face value, with the full face value repaid at maturity.

Par Value

The nominal or face value of a bond, share of stock, or other financial instrument, as stated by the issuer.