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https://www.math.colostate.edu/~clayton/teaching/m113f09/homework/hw2solutions.pdf#:~:text=26%3A%20A%20bacterial%20culture%20starts%20with%20500%20bacteria,have%20doubled%206%20times.Therefore%2C%20there%20will%20be500%C2%B726%3D%2032%2C000
http://www.math.utep.edu/Faculty/cmmundy/Math%201320/Worksheets/Solutions/Chapter%209/9.2/9.2%20question%205.pdf
A bacteria culture starts with 1,000 bacteria and doubles in size every 3 hours. Find an exponential model for the size of the culture as a function of time t in hours. Solution: Use the formula ๐ฆ=๐ด๐๐ก (example 4 on p. 636 is similar). The starting amount of bacteria is 1000, so ๐ด=1000.
https://socratic.org/questions/the-number-of-bacteria-in-a-certain-culture-doubles-every-3-hours-if-there-are-n
https://socratic.org/questions/a-bacteria-culture-starts-with-500-bacteria-and-doubles-in-size-every-3-hours-ho
https://www.quora.com/The-number-of-bacteria-in-a-certain-culture-doubles-every-3-hours-if-there-are-100-bacteria-to-start-with-What-is-the-number-in-24-hours
The number of bacteria in the culture doubles every three hours. The number of bacteria B is given by B = 100 x 2^^N, where N is the number of doublings that have taken place since the time when the bacteria were known to number 100. N = H/3, H being the number of hours that have passed. N = 24/3 = 8. There have been 8 doublings in 24 hours.
https://www.quora.com/A-culture-of-bacteria-doubles-every-two-hours-If-there-are-500-bacteria-at-the-beginning-how-many-bacteria-will-there-be-after-24-hours-How-do-I-write-this-as-a-geometric-series
The number of bacteria in the culture doubles every three hours. The number of bacteria B is given by B = 100 x 2^^N, where N is the number of doublings that have taken place since the time when the bacteria were known to number 100. N = H/3, H being the number of hours that have passed. N = 24/3 = 8.
https://www.tsfx.com.au/wp-content/uploads/2018/04/N5-PreCalc6_04_06-Compatibility-Mode.pdf
Exponential Growth (Doubling Time) Suppose we start with a single bacterium, which divides every hour. After one hour we have 2 bacteria, after two hours we have 22 or 4 bacteria, after three hours we have 23 or 8 bacteria, and so on (see Figure 1). We see that we can model the bacteria population after t hours by f(t) = 2t. Bacteria population Figure 1
https://www.alamo.edu/contentassets/3c031ab72f3d4dbda979bc9e66d11634/exponential/math1414-exponential-growth-and-decay.pdf
ln(2) 0.91629 t t t e e e t t = = = = = t โ0.756 . Thus, the bacteria count will double in about 0.75 hours. Solution (b): Using the population growth function found in part (a), with rate . r = 0.91629 and time t = 3, we find . ne (3) 10,000 0.91629(3) 156,249.66 = โ. So, the number of bacteria after 3 hours is about 156,250. Radioactive Decay:
http://www.math.utep.edu/Faculty/cmmundy/Math%201320/FAQ/Exponential%20Growth%20solution.pdf
bacteria is 1000, so ๐ด=1000. To find ๐, plug in 2 for ๐ก and 2000 for ๐ฆ (since the population doubles in 2 hours): 2000=1000๐2, divide both sides by 1000 to get 2=๐2. Raise both sides to the 1โ2power to get 21โ 2=(๐)1โ2, so ๐=21โ2. Thus, the function is ๐ฆ=1000(21โ2) ๐ก, or ๐ฆ=1000(2๐กโ2).
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