Question

Please help my brain is so confused.

The population of blue-green algae in a certain lake is increasing at a rate of 33% per hour. The count was at 5,000 cells per milliliter at noon on August 1. By what date and time will the algae count get to the "high alert" level of 50,000 cells per milliliter? Assume that the algae continues to increase at the same rate.

a)12:00 noon August 9
b) 8:00am august 21
c)8:00 pm august 1
d)12 midnight august 30

Answer 1

Total = 5,000*(1.33)^hours
That should help you out.

Answer 2

thank you so much.

Answer 3

u r welcome

Answer 4

would the answer be d?

Answer 5

Test the formula to see how much remains after 24 hours.

Answer 6

your "danger level" is 10x the starting level. that means that after some number of hours, \(t\), \[1.33^t = 10\]
because the \(1.33^t\) is the part of the expression that provides the growth.

Answer D is midnight on August 30, which is 12 hours and 29 days later, or 708 hours later. For that to be correct, \[1.33^{708}\approx 10\]In fact, even if the growth rate was only 0.33% (1/100th of the rate actually given), that would still get you to 10x the starting amount. With the value given in the problem? Your new population would be \(2.4*10^{91}\) cells per milliliter! That's impossible, of course, as that is larger by many orders of magnitude than the number of atoms in the observable universe...