Question 185120: I am having trouble with a logarithmic bacteria word problem.
A bacterial culture is growing according to the formula y=50,000e^0.8x. In this formula, x is the time in days and y is the number of bacteria. Estimate the number of bacteria after 1 month. (Hint: Assume there are 30 days in a month.)
I am the teacher for my son and do not know how to solve this. The answer is y = 1.324456 x 10^15. Please help.
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
Substituting 30 for x makes the exponent 0.8 times 30 = 24, so:
e is the base of the natural logarithms, approximately 2.718.
So, unless you are some sort of arithmetic masochist, and want to multiply 2.718 times itself 24 times, it is time to get out the calculator.
Using the Windows built-in calculator in Scientific mode, enter 24, click the Inv check box in the upper left corner, then click the 'ln' button (e raised to a power is the inverse of taking the natural logarithm, ln). Then click '*', enter 50000, and click '='.
If you have Excel on your computer, open a sheet and enter the following in a cell:
=50000*exp(24)
Then press enter.
John
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