What is the Exponential Growth?

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asked 2021-02-16

The number of teams y remaining in a single elimination tournament can be found using the exponential function \(\displaystyle{y}={128}{\left({\frac{{{1}}}{{{2}}}}\right)}^{{x}}\) , where x is the number of rounds played in the tournament. a. Determine whether the function represents exponential growth or decay. Explain. b. What does 128 represent in the function? c. What percent of the teams are eliminated after each round? Explain how you know. d. Graph the function. What is a reasonable domain and range for the function? Explain.

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asked 2021-01-06

The current student population of Tucson is 2900. If the population increases at a rate of 14.8% each year. What will the student population be in 7 years?
Write an exponential growth model for the future population P(x) where x is in years:
P(x)=
What will the population be in 7 years? (Round to nearest student)

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asked 2021-02-08

A "Student Drug Use and Health Survey" of Ontario high school students found that the percentage of students that reported serious psychosocial distress in the past month increased from 10.7% in 2013 to 17.1% in 2017.
Assuming a standard exponential growth trend, what is the annual growth rate in the percentage of students reporting serious psychosocial distress in the past month?

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asked 2021-02-09

A regional rail company wants to reduce its delays. Presently, 70 percent of the trains arrive on time. The company’s goal is to improve this to 95 percent. What form of improvement trajectory will most likely occur?
a. Exponential growth
b. Exponential decay
c. Diminishing return growth

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asked 2020-11-24

In the exponential growth or decay function y=y0e^kt, what does y0 represent? What does k represent?

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asked 2021-02-02

Describe what the values of C and k represent in the exponential growth and decay model y=Ce^kt

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asked 2020-11-08

In 2005, the population of a district was 28,300, With a continuous annual growth rate of approximately 7% what will the population be in 2020 according to the exponential growth function? Round the answer to the nearest whole number.

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asked 2020-12-17

In 2017, the population of a district was 20,800. With a continuous annual growth rate of approximately 6%, what will the population be in 2032 according to the exponential growth function?
Round the answer to the nearest whole number.

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asked 2020-10-23

The close connection between logarithm and exponential functions is used often by statisticians as they analyze patterns in data where the numbers range from very small to very large values. For example, the following table shows values that might occur as a bacteria population grows according to the exponential function P(t)=50(2t):
Time t (in hours)012345678 Population P(t)501002004008001,6003,2006,40012,800
a. Complete another row of the table with values log (population) and identify the familiar function pattern illustrated by values in that row.
b. Use your calculator to find log 2 and see how that value relates to the pattern you found in the log P(t) row of the data table.
c. Suppose that you had a different set of experimental data that you suspected was an example of exponential growth or decay, and you produced a similar “third row” with values equal to the logarithms of the population data.
How could you use the pattern in that “third row” to figure out the actual rule for the exponential growth or decay model?

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asked 2021-01-06

Write an exponential growth or decay function to model each situation. Then find the value of the function after the given amount of time. The student enrollment in a local high school is 970 students and increases by 1.2% per year, 5 years.

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Answer 1

Exponential Growth is a type of growth of any quantity over a specific period of time. The term exponential is derived from the word exponent which means power. Therefore exponential growth is defined as the rate change i.e. change with respect to time of any quantity which is proportional to itself.
For example Alpha decay, the growth of bacteria
Graph

\(f(x)=e^x\) is a type of exponential function. The graph of which can be demonstrated as,

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What is the Exponential Growth?

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