Write a System of Linear Equations in Three Variables, and Then

question 114

Multiple Choice

Write a system of linear equations in three variables, and then use matrices to solve the system.
-The table below shows the number of birds for three selected years after an endangered species protection program was started. $$\begin{array} { l | c c c } \mathrm { x } \text { (Number of years after 1980) } & 1 & 5 & 10 \\\hline \mathrm { y } \text { (Number of birds) } & 43 & 139 & 349\end{array}$$ Use the quadratic function $y = a x ^ { 2 } + b x + c$ to model the data. Solve the system of linear equations involving $a , b$ , and $c$ using matrices. Find the equation that models the data.

• A) \(y = 2 x ^ { 2 } + 12 x + 29\)
• B) \(y = 3 x ^ { 2 } + 24 x + 24\)
• C) \(y = 4 x ^ { 2 } - 12 x + 32\)
• D) \(y = 4 x ^ { 2 } - 36 x + 25\)

---

Definitions:

Payments

Payments refer to the amounts of money transferred from one party to another as compensation for goods or services, or as fulfillment of an obligation.

Compounded Quarterly

The process where interest is added to the principal sum of a loan or deposit four times a year, resulting in a higher amount of interest being accumulated than if compounded less frequently.

Equivalent Economic Position

A financial strategy or situation where two different financial instruments or situations have the same economic value or return.

Payments

Transactions or exchanges of money between two parties, often for goods or services rendered.