Exponential Function: Understanding and Solving Problems

AI Thread Summary
To solve problems involving exponential functions, identify the function as f(x)=ax, where 'a' is the ratio between data entries. Calculate the ratio by dividing consecutive data points and averaging these ratios to find missing values. For example, using case numbers for H1N1, the ratios between days can be calculated to illustrate the exponential growth. Plotting the data on semilog graph paper can help visualize the relationship, as the curve of best fit should appear as a straight line, allowing for slope measurement to derive the function. The original poster did not engage in problem-solving despite multiple responses, leading to the closure of the thread.
schan11
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Help! exponential function

Please look at the attachment for the question!

Thank you for your help
 

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An exponential function is a function f(x)=ax, where a is the ratio between entries. Since you have a bunch of data, divide between entries to find the ratio, a. Then average them to get the average ratio, and use this average ratio to find the missing values.
 


Harrisonized said:
An exponential function is a function f(x)=ax, where a is the ratio between entries. Since you have a bunch of data, divide between entries to find the ratio, a. Then average them to get the average ratio, and use this average ratio to find the missing values.

But how do you work out the function?
 


Let's take the first two entries as an example.

On day 21/5, we have 3 cases of H1N1. On day 22/5, we have 7 cases of H1N1.

What's 7/3? 2.333.

On day 22/5, we have 7 cases of H1N1. On day 23/5, we have 12 cases of H1N1.

What's 12/7? 1.714.

Hopefully by now you've noticed that these are the values in the third column.
 


schan11 said:
Please look at the attachment for the question!
It might be instructive to plot the raw data on semilog graph paper. (Search on google, and print out a sheet of it.) The curve of best fit should be a straight line. Measure its slope. From this you can work out the equation you seek. This should support the figures in the right-most column of your data. This exercise amounts to graphically taking an average of the numbers in the right column, and, if it hadn't already been done, would save calculating those numbers.
 
Last edited:


Even after several responses, there is no attempt at all by the original poster to work the problem himself. Thread closed.
 

Thread 'Family of lines that are at a distance of 5 from the origin'

I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...
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