If anyone does this lol idk but im not gonna look at this because im already done (with the first and second task)
Task 1
Bacteria are the most common example of exponential growth. Research and find a
bacterium that grows each hour exponentially and determine how much it grows
per hour.
a. Suppose you start with one single bacterium. Make a table of values showing
the number of bacteria that will be present after each hour for the first six
hours. Then determine how many bacteria will be present once 24 hours
have passed.
b. Explain why this table represents exponential growth.
c. Using this example, explain why any number raised to a power of zero is
equal to one.
d. Write a rule for this table.
e. Suppose you started with 100 bacteria, but they still grew by the same
growth factor. How would your rule change? Explain your answer.
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)?
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