SOLUTION: 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

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

RELATED QUESTIONS
a bacterial culture is growing exponentially according to the equation y= 250e ^0.07t... (answered by Boreal)

Solve the problem. The number of bacteria growing in an incubation culture increases... (answered by KMST)

The number bacteria growing in an incubation culture increases with time according to... (answered by josmiceli,josgarithmetic,MathTherapy)

Solve the problem. The number of bacteria growing in an incubation culture increases... (answered by stanbon)

A staphylococcus bacterial culture grows according to the formula P=P(sub o)a^t. if it... (answered by jsmallt9)

A bacterial culture grows according to the formula P=Poa^t. If it takes 5 days for the... (answered by scott8148)

A bacterial culture contains 800 bacteria initially and double every 90 minutes. The... (answered by Cromlix)

One bacterial culture is 18 days older than a second bacterial culture. In 10 days the... (answered by Greenfinch)

The number of bacteria in a culture is increasing according to the law of exponential... (answered by ankor@dixie-net.com)