Given:
The lake started with only 4 square feet infected.
The bacteria are growing by a factor of 3 every hour.
To find:
The domain for this situation.
Solution:
Initial value = 4 square feet
Growth factor = 3
Using exponential growth model, we get
[tex]y=ab^t[/tex]
where, a is initial value and b is growth factor.
So, square feet of bacteria after t hours is
[tex]y=4(3)^t[/tex]
Here, domain is set of values of time and range is square feet of bacteria.
Above equation is defined for all values of t but we know that, time cannot be negative.
As the relationship between hours and square feet of bacteria is continuous, therefore the value of t can be any real number greater than or equal to 0.
[tex]Domain=\{t|t\in R\text{ and }t\geq 0\}[/tex].
Therefore, the domain is [tex]\{t|t\in R\text{ and }t\geq 0\}[/tex].
