I am working on a problem about bacteria growing and I used my calculator to find the exponential equation to be y = 10006.06771(1.2297)^x
First it asked how many bacteria would there be after 6 hours which was easy because I just plugged in 6 for x and that was about 34,599 bacteria.
But now the question is how long will it take until there are 100,000 bacteria. I know I need to use my calculator to determine this on a table, but I don't know how.....
NVM - I think I figured it out - thank you anyway
10006.06771(1.2297)^x = 100000
1.2297^x = 9.993936
x = log9.993936/log1.2297
To determine how long it will take until there are 100,000 bacteria, you need to find the value of x that makes y equal to 100,000 in the exponential equation.
Here's how you can use your calculator to determine this:
1. Start by plugging in various values of x into the equation given, starting with small increments (e.g., x = 1, 2, 3, ...).
2. Calculate the corresponding values of y for each x value to create a table. You can do this by entering the equation into your calculator, inputting the x values, and hitting the "enter" or "equals" button.
3. Keep calculating the values of y until you find the one that is closest to 100,000. Note the corresponding x value for this y value.
4. As you approach the value of 100,000, the intervals between the x values can become smaller to increase the accuracy. For example, if the y values around 100,000 are 99,700, 100,050, and 99,900, you can try inputting x values of 6.1, 6.05, and 6.15 to find the closest x value for which y is approximately equal to 100,000.
5. Once you find the x value closest to y = 100,000, you have found the approximate time it will take until there are 100,000 bacteria.
Remember that since exponential growth is continuous, the value of x you find will be an approximation, not an exact answer.
By following these steps, you should be able to use your calculator to determine how long it will take for there to be 100,000 bacteria.