Task 2
a. do some research and find a city that has experienced population growth.
determine its population on january 1st of a certain year. write an
exponential function to represent the city’s population, y, based on the
number of years that pass, x after a period of exponential growth. describe
the variables and numbers that you used in your equation.
b. find another city whose population starts larger than the city in part (a), but
that during this same time experienced population decline. determine its
population for january 1st of the same year you picked for part (a). write an
exponential function to represent the city’s population, y, based on the
number of years that pass, x after a period of population decline. describe
the variables and numbers that you used in your equation.
c. explain the similarities and differences between your equations in (a) and
(b).
d. during what year will the population of city (a) first exceed that of city (b)?
show all of your work and explain your steps.
e. during what year will the population of city (a) be at least twice the size of
the population of city (b)? show all of your work and explain your steps.
task 3
greece is currently experiencing a financial crisis.
a. research the financial crisis in greece and summarize it in one-two
paragraphs.
b. you are in charge. by what percentage will you tell greece to cut their
spending? what is the decay factor?
c. write a function modeling this debt situation if the initial debt in 2009 was
$500 billion and using the decay factor found in (b). let y be measured in
billions of dollar and x represent the number of years since 2009.
d. when will greece be debt-free if you are in charge? should you reconsider
your answer to (b)?

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)

b. 6

step-by-step explanation:

we are given the table representing an exponential function.

we can see from the table that, as x is increasing, the value of y is increasing in the power of 6.

i.e. the following relation is obtained,

x = 1, y = 6

x = 2, y = 36 =

x = 3, y = 216 =

x = 4, y = 1296 =

x = 5, y = 7776 =

so, the geometric series obtained is .

thus, the common ratio is given by = = 6.

hence, the common ratio is 6.

$655.61 which is option c

step-by-step explanation:

price of house =   $146,000

initial rate = 3.5%

mortgaged paid in this = 3.5 % of $146,000

                                        =

                                        =$5110

the total years would be = 7

total mortgaged paid = 7 * $5110

                                      =$35770

remaining money = $146000-35770

                                =$110230

new mortgaged payment = 5 % of 110230

                                            =  

                                            =$655.61