Hello,
I am working on exponential equations of best fit. I have a table numbered from 1-7 with corresponding numbers.
I put that into my calculator and came up with the exponential equation of best fit as y = 8.46(1.42)^x
Now it wants to know how long it will take for 200 items to be sold.
So I know my y is 200 and I set it up as this:
200 = 8.46(1.42)^x
But how do I solve this??
My table only goes up to 7 in my L1 listing, and that is only 96, not 200. So how do I get my L1 to go more than what I have entered?
Thank you.
200/8.46 = 8.46*(1.42)^x/8.46,
23.64 = (1.42)^x,
Log23.64 = x*Log1.42,
X = Log23.64/Log1.42 =
This is in addition to Henry's approach, in case you haven't learned logarithms yet.
I don't know what kind of graphing calculator you are using, but it sounds like you entered the data in the STAT area of your calculator, which is correct for finding the equation.
Now that you have the equation, it should also appear in the "Y=" list, if you saved it there. If you did, you can use the table setup function (TBLSET) and set it to start at any x value, increasing in steps of any value you choose. Then view it (TABLE). That table will display x and y values for your equation and will scroll down to as far as you need.
To solve the equation 200 = 8.46(1.42)^x, you are looking for the value of x that satisfies this equation. Since you mentioned that your table only goes up to 7 and reaches a maximum value of 96, you need to find a way to extend the values to include x = 200.
One way to do this is to use your calculator to calculate the values of y = 8.46(1.42)^x for additional x-values. Here's how you can do it:
1. To extend your table, you can manually calculate the values of y for x = 8, 9, 10, and so on, until you reach an x-value close to or greater than 200. Plug these values of x into your equation and solve for y using your calculator.
For example, for x = 8, you can calculate y as follows:
y = 8.46(1.42)^8
2. Alternatively, you can use the exponential function feature in your calculator to generate the table for you. Most scientific calculators or graphing calculators have this functionality. Look for an exponential function feature or an option to generate a table of values.
Once you have obtained the values of y for these additional x-values, you can look for the x-value that corresponds to y = 200. Now, depending on the accuracy you require, you might need to interpolate between the given values in your table or use trial and error to find the specific x-value that results in y = 200.