The Lake of Distress is contaminated with flesh-eating bacteria!! The lake started with only 4 square feet infected, but as time has gone on, the bacteria are growing by a factor of 3
every hour. Assume that the relationship between hours and square feet of bacteria is
continuous.

What is the domain of the function in set notation?

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

where, a is initial value and b is growth factor.

So, square feet of bacteria after t hours is

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.

.

Therefore, the domain is .

3201

step-by-step explanation: