FUNCTION MODELLING

Question 1

The population of Manhattan Island in New York City between 1890 to 1970 can be modeled by 𝑃(𝑥) = −0.78𝑥4+133𝑥3 −7500𝑥2+147,500𝑥 + 1,440,000, where P(x) represents the population and x represents the number of years since 1890.

A. Use the model to predict the population in 1980.

Answer 1

-253800

Question 2

The population of Manhattan Island in New York City between 1890 to 1970 can be modeled by 𝑃(𝑥) = −0.78𝑥4+133𝑥3 −7500𝑥2+147,500𝑥 + 1,440,000, where P(x) represents the population and x represents the number of years since 1890.

B. According to this model, what happens between 1970 and 1980?

Answer 2

Population becomes 0

Question 3

A doctor tells Masa to take 60 milligrams of medication each morning for three days. The amount of medication remaining in his body on the fourth day is modeled by M(x) = 60x3 + blablabla

A. Write an equation to model this situation

Answer 3

37.44=60x3 + 60x2+ 60x

Question 4

A doctor tells Masa to take 60 milligrams of medication each morning for three days. The amount of medication remaining in his body on the fourth day is modeled by M(x) = 60x3 + blablabla

B. Write the related function for the equation

Answer 4

60x3 + 60x2+ 60x - 37.44

Question 5

A doctor tells Masa to take 60 milligrams of medication each morning for three days. The amount of medication remaining in his body on the fourth day is modeled by M(x) = 60x3 + blablabla

C. estimate the absorption rate

Answer 5

about 1/2

Question 6

A doctor tells Masa to take 60 milligrams of medication each morning for three days. The amount of medication remaining in his body on the fourth day is modeled by M(x) = 60x3 + blablabla

find the absorption rate of the medication

Answer 6

0.4

Question 7

in the early 1900s, the dee population of the kaibab plateau in Arizona experienced aors. The food supply was not great enough to support the increased population, eventually causing the population to decline. The deer population for the period 1905 to 1930 can be modeled by 𝑓(x) = basta equation

A. use the model to determine the population in 1905

Answer 7

4000 deers

Question 8

in the early 1900s, the dee population of the kaibab plateau in Arizona experienced aors. The food supply was not great enough to support the increased population, eventually causing the population to decline. The deer population for the period 1905 to 1930 can be modeled by 𝑓(x) = basta equation

b. use the model to determine the population in 1920

Answer 8

67281 deers

Question 9

in the early 1900s, the dee population of the kaibab plateau in Arizona experienced aors. The food supply was not great enough to support the increased population, eventually causing the population to decline. The deer population for the period 1905 to 1930 can be modeled by 𝑓(x) = basta equation

c. according to this model when did the deer population become zero

Answer 9

1930

Question 10

the regression equation for a set of data is y=-3.54x-710.7 where x represents the year and y represents the average number of students assigned to each advisor in a certain business school. use the equation to predict the number of students assigned to each adviser in the year 2005

Answer 10

10 students

Question 11

the percent of United States population living in the metropolitan areas has increased since 1950

table

A. Use the model to predict the percent of the population that will be living in metropolitan areas in 2010

Answer 11

87.1%

Question 12

the percent of United States population living in the metropolitan areas has increased since 1950

table

B. what year will have 85% of the poppultion

Answer 12

2006

Question 13

The United States Census Bureau has projected the median age of the U.S. population to the year 2080. A fast-food chain wants to target its marketing toward customers that are about the median age.

A. what age the fast-food chain should target in the year 2005

Answer 13

36

Question 14

The United States Census Bureau has projected the median age of the U.S. population to the year 2080. A fast-food chain wants to target its marketing toward customers that are about the median age.

b. what age the fas-food chain should target in 2025

Answer 14

38

Question 15

the attendance of major league baseball games for various years is listed below

tale

When will the attendance reach 71 million again

Answer 15

2000

Question 16

luisa diaz is planning to build a new factory for her business. she hires an analyst to gather data and develop a mathematical model. in the model, blablabla, is ms. diaz’s monthly profit. blablabala

A. How many employees should she hire to amximire profits

Answer 16

23 employess

Question 17

luisa diaz is planning to build a new factory for her business. she hires an analyst to gather data and develop a mathematical model. in the model, blablabla, is ms. diaz’s monthly profit. blablabala

B. what is her maximum profit

Answer 17

$1076