a colony of 300 bacteria doubles each day. write an explicit formula to determine how many bacteria there would be on the nth day. how would you do this?

amount = 300(2)^n , where n is the number of days.

so on the nth day you would have 300(2)^n

To determine the number of bacteria on the nth day, we can use the explicit formula for exponential growth.

The formula for exponential growth is given by:

P(n) = P(0) * (1 + r)^n

In this formula:
- P(n) represents the population size on the nth day.
- P(0) represents the initial population size.
- r represents the growth rate.
- n represents the number of days.

In this case, the initial population size is 300, and the population doubles each day. The growth rate (r) can be calculated using the growth factor. Since the population doubles, the growth factor is 2 (1 + 100%).

Substituting these values into the formula, we get:

P(n) = 300 * (2)^n

So, the explicit formula to determine the number of bacteria on the nth day is P(n) = 300 * (2)^n.

To determine the number of bacteria on the nth day, you can use the concept of exponential growth. Since the colony doubles each day, the growth is exponential.

To create the explicit formula for this growth, let's first consider the initial population of bacteria (300). We can express the population at the end of each day as a function of the number of days passed.

Let P(n) represent the population of bacteria on the nth day. We can observe that the population doubles each day, so we can express the growth as: P(n) = P(0) * 2^n, where P(0) represents the initial population (300).

Therefore, the explicit formula to determine the number of bacteria on the nth day is:

P(n) = 300 * 2^n

To find the number of bacteria on a given day (n), simply substitute the value of n into the formula. For example, to find the number of bacteria on the 5th day, substitute n = 5 into the formula:

P(5) = 300 * 2^5
= 300 * 32
= 9,600

So, on the 5th day, there would be 9,600 bacteria in the colony.