In the exponential patterns, the successive numbers increase or decreases by the same percent.
Exponential growth patterns: A sequence of numbers has an exponential pattern when each successive number increase by the same percentage.
There is one simple example of a sequence of an exponential growth:
The population of a dogs doubled every year and the sequence is given as:
2, 4, 8, 16, 32, 64, 128, 256 etc.
In the exponential function, over the time t values of function increase very fast.
Now, the formula for exponential growth function is:
\(y(t)=ae^{kt}\)
\(a=\)initial value
\(t=\)time
\(k=\)rate of growth
\(y(t)=\)value at time t
Question
Create an example of sequence of numbers with an exponential growth pattern, and explain how you know that the growth is exponential.
Answers (1)
2021-03-07
Relevant Questions
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?
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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Determine whether each function is an example of exponential growth or decay. Then find the y-intercept. \(\displaystyle{y}={0.1}{\left({10}\right)}^{{x}}\)
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