1. The table shows the number of wild strawberry plants in a particular forest t years after a forest fire. Use a graphing calculator to find the exponential function that best fits the set of data.
Number of Wild Strawberry Plants
years | wild strawberry plants
0 34
1 136
2 544
3 2176
4 8704
5 34816
the answer is: S = 34(4)t
how am I supposed to be able to figure out the answer?
thanks!
34 * 4 = 136. The same relationship continues each year, so for t years, it would be 34(4)t.
This was found without the use of a calculator.
I hope this helps. Thanks for asking.
I mean, how would I figure it out if I didn't already know the answer?
Unfortunately, I do not have a graphing calculator, so I cannot help you there. Sorry.
I find it rather silly to have a question that asks for the use of a graphing calculator to find the equation of "best fit" when the data is exact and follows such an obvious pattern.
It follows a geometric sequence with the first term 34 and a common difference of 4
it is easy to see why the exponential equation has to be
No of Strawberries = 34(4)^time
graphing programs have built-in programs which allow for the data values to be entered as a matrix.
Since that varies from one calculator to the next, I don't think anybody can help your with the "how To" of that.
If you are using the texas Instrument series of calculator, you want to insert he numerical data point into the "List" section on your calculator... This is a yellow wording above one of your keys... enter the info here... Then go to stat, calc, expreg and let it do it's magic :-)
thanks
You're welcome! I apologize for the confusion earlier. I understand now that you were looking for guidance on how to find the exponential function without prior knowledge of the answer.
To find the exponential function that best fits the given data points, you can follow these steps:
1. List the given data points in two lists, one for the years and one for the number of wild strawberry plants. For example:
Years: 0, 1, 2, 3, 4, 5
Plants: 34, 136, 544, 2176, 8704, 34816
2. On your graphing calculator, go to the "STAT" or "STATS" menu, depending on your calculator model.
3. Enter the years in the first list and the number of plants in the second list.
4. Once the data is entered, go to the "CALC" or "STAT CALC" menu. Look for an option that says "ExpReg" or "Exponential Regression". This option will calculate the equation of the exponential function that best fits the data.
5. Select the "ExpReg" or "Exponential Regression" option and let the calculator calculate the exponential function.
The result should give you the equation of the exponential function that best fits the data. In this case, it should be:
Number of Strawberries = 34(4)^t
I hope this clarifies the process for you. Let me know if you have any further questions!
You're welcome! I apologize for any confusion caused by my previous response.
To clarify, if you didn't already know the answer, you could still determine the exponential function that best fits the data by analyzing the pattern.
Looking at the given data, you can observe that the number of wild strawberry plants is increasing by a factor of 4 each year. This means that for each year that passes, the number of plants is multiplied by 4.
For example, starting with 34 plants in year 0, in year 1 there are 34 * 4 = 136 plants. In year 2, there are 136 * 4 = 544 plants, and so on.
Based on this pattern, you can determine that the exponential function that best fits the data is of the form S = 34(4^t), where S represents the number of wild strawberry plants and t represents the number of years after the forest fire.
So, even without a graphing calculator, you can analyze the data and recognize the pattern to arrive at the correct exponential function.