Answer:
[Tex]A(t)=5000(0.7)^t[/tex]
Step-by-step explanation:
The problem presented is one in which the population of the bacteria depreciates by a decay factor r every year.
Since it is a decay problem, we use the model:
[Tex]A(t)=P(1-r)^t[/tex]
Initial Population, P=5000
Decay Rate,r=30%=0.3
t=time interval
Therefore, the equation that represents this situation is:
[Tex]A(t)=5000(1-0.3)^t[/tex]
[Tex]A(t)=5000(0.7)^t[/tex]
The equation that represents this situation is y = 5000(0.7)ˣ
An exponential decay is given by:
y = abˣ
where a is the initial value of y, b is the rate of decay and y, x are variables.
Since the culture begins with 5000 cells, hence a = 5000. The cells die by 30% each year, hence b = 100% - 30% = 0.7
The equation is: y = 5000(0.7)ˣ
Therefore the equation that represents this situation is y = 5000(0.7)ˣ
Find out more at: https://brainly.com/question/14355665
