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Exponential Decay
hour Number of Bacteria
250
62.5
3.91
10
0.97
The population change of bacteria in a pond is shown in the table.
Which graph shows a rate of change that is similar to the rate of change of the bacteria?

Exponential Decay hour Number of Bacteria 250 625 391 10 097 The population change of bacteria in a pond is shown in the table Which graph shows a rate of chang class=

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opudodennis

Answer:

c. Exponential decay with the function [tex]A=A_oe^{-0.3466t}[/tex]

Step-by-step explanation:

#We plot our values in Excel. The plot output is an exponential decay graph.

[tex]A=A_oe^{kt}\\\\A_o-initial \ value\\A=ending \ value\\e-exponent value\\k-continous \ decay \ rate\\\\t-time[/tex]

Take any two values from our data to determine the k decay rate:

[tex]A=A_oe^{kt}, A_o-250, A-62.5, t=4\\\\62.5=250e^{4k}\\\\4k=In 0.25\\\\k=-0.3466[/tex]

Hence, the function for exponential decay is given as:

[tex]A=A_oe^{-0.3466t}[/tex]

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