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

B. Saginaw, Michigan:
51,413
51,043
50,763
50,303

A. Salem Oregon:
155,094
156,273
159,282
160,614

Hey dudes,

Here's my work for Task 1 of this portfolio. Hope it helps!\
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 using the hourly growth rate that you selected. Then determine how many bacteria will be present once 24 hours have passed.
I chose the number 3.
Number of Hours Number of Bacteria
0 1
1 3
2 9
3 27
4 81
5 243
6 729
After 24 hours, there will be 282,429,536,481 bacteria
Explain why this table represents exponential growth.
This table represents exponential growth because the number of bacteria is always multiplied by 3.
Using this example, explain why any nonzero number raised to a power of zero is equal to one.
The reason any nonzero number raised to power of zero equals one is that any number to the zero power is the product of no numbers, which is multiplicative identity 1.
Write a rule for this table.
y=1×3^x
Suppose you started with 100 bacteria, but they still grew by the same growth factor. How would your rule change? Explain your answer.
I would change the rule into y=100×3^x.
My first rule started from 1 bacterium, and would multiply by 3 for x times. Now that I am starting with 100 bacteria but still using the same growth factor (3x), I would change 1 from my earlier rule into 100, but keep the remaining values same.

:) ~Anonymous
(P.S., I got 100% on this part. I usually send my portfolio in separate documents. This one was for Task 1. If I get positive feedback on the rest, I will share it with you. Maybe.)

P.P.S., If I do not come back, pleeeeeaaase forgive me!

not helpful.

To find a city that has experienced population growth and determine its population on January 1st of a certain year, you can use publicly available data or reliable sources such as government databases, statistical reports, or reputable news articles. Let's use Salem, Oregon as an example.

Based on the given data, the population of Salem, Oregon on January 1st of a certain year is as follows:

January 1st, Year 1: 155,094
January 1st, Year 2: 156,273
January 1st, Year 3: 159,282
January 1st, Year 4: 160,614

To write an exponential function representing the city's population growth, we can use the general form of an exponential function: y = ab^x, where y is the population, x is the number of years after a period of exponential growth, a is the initial population (when x = 0), and b is the growth factor or the rate at which the population grows.

To find the values of a and b, we can use the given population data.

Using the first set of data:
a = 155,094 (population on January 1st, Year 1)
x = 0 (since it's the initial population)
y = 155,094
Plugging these values into the exponential function, we get: 155,094 = ab^0. Simplifying, we have: a = 155,094.

Using the second set of data:
a = 155,094 (population on January 1st, Year 1)
x = 1 (1 year has passed since the initial population)
y = 156,273
Plugging these values into the exponential function, we get: 156,273 = 155,094b^1. Simplifying, we have: b = 156,273/155,094.

Using the third set of data:
a = 155,094 (population on January 1st, Year 1)
x = 2 (2 years have passed since the initial population)
y = 159,282
Plugging these values into the exponential function, we get: 159,282 = 155,094b^2.

Using the fourth set of data:
a = 155,094 (population on January 1st, Year 1)
x = 3 (3 years have passed since the initial population)
y = 160,614
Plugging these values into the exponential function, we get: 160,614 = 155,094b^3.

Now, we have a system of equations. Solve this system of equations to find the value of b:

155,094b^1 = 156,273
155,094b^2 = 159,282
155,094b^3 = 160,614

By dividing each equation by 155,094 and isolating b, you can find the value of b. Once you have the value of b, you now have the exponential function representing the city's population growth.

dcs