math problem solving

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Task 1Bacteria are the most common example of exponential growth. Select a numberbetween 2 and 10 to represent the hourly growth rate of a certain bacteria. Forexample, selecting the number 8 would mean that the amount of bacteria will be 8times greater after every hour.a. Suppose you start with one single bacterium. Make a table of values showingthe number of bacteria that will be present after each hour for the first sixhours using the hourly growth rate that you selected. Then determine howmany bacteria will be present once 24 hours have passed.b. Explain why this table represents exponential growth.c. Using this example, explain why any nonzero number raised to a power ofzero is equal to one.d. Write a rule for this table.e. Suppose you started with 100 bacteria, but they still grew by the samegrowth 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 citys 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 citys 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.

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