Question

This was an exceptionally dry year for portions of the southwestern United States. Monthly precipitation in Phoenix, Arizona, was recorded in the table and is modeled by y = –0.04088x2 + 0.4485x + 1.862.

In what month did Phoenix receive the lowest amount of precipitation?

Month (x) Precipitation
January 2.27 inches
February ?
March ?
April ?
May ?
June ?
July ?
August ?
September 2.59 inches
October ?
November ?
December ?

Sketch a graph or fill in the table to answer the question.
A) January
B) February
C) November
D) December

Answer 1

D

Explanation:

y = -0.04088x^2 + 0.4485x + 1.862

y is the amount of precipitation,

x is the month (1 for January, 2 for February, etc.)

The amount of precipitation from Jan to Dec are listed below

(generated with R language, a handy software)

2.26962 2.59548 2.83958 3.00192 3.08250 3.08132 2.99838 2.83368 2.58722 2.25900 1.84902 1.35728

The month with lowest precipitation is December

Answer 2

D) December

Explanation:

The given equation to model the monthly precipitation in Phoenix, Arizona is:

`y = -0.04088x^2 + 0.4485x + 1.862`

where:

• y is the monthly precipitation (in inches).
• x is the number of the month (January = 1).

To determine the month in which Phoenix received the lowest amount of precipitation, fill in the table by inputting each value of x into the equation. Round the value of y to 2 decimal places.

`\begin{array}l\cline{1-3}&x&y\\\cline{1-3}\sf January &1&2.27\\\cline{1-3}\sf February &2&2.60\\\cline{1-3}\sf March &3&2.84\\\cline{1-3}\sf April &4&3.00\\\cline{1-3}\sf May &5&3.08\\\cline{1-3}\sf June &6&3.08\\\cline{1-3}\sf July &7&3.00\\\cline{1-3}\sf August &8&2.83\\\cline{1-3}\sf September &9&2.59\\\cline{1-3}\sf October & 0&2.26\\\cline{1-3}\sf November &11&1.85\\\cline{1-3}\sf December &12&1.36\\\cline{1-3}\end{array}`

Reading from the table, the month in which Phoenix received the lowest amount of precipitation was December, when only 1.36 inches of precipitation was recorded.