Answer:

3:22 PM
Explanation:
To write an exponential growth equation to represent the number n of cells in the dish after t minutes, we can use the exponential function formula:

Let the number of bacteria at 1:00 PM be the initial value, so a = 85.
The number of minutes, t, is the independent variable, so x = t.
The number of cells, n, is the dependent variable, so y = n.
Substituting these values into the formula, we get:

where:
- n is the number of bacteria cells.
- t is the time (in minutes) after 1:00 PM.
We are told that after 75 minutes, the number of bacteria is 1050.
Therefore, when t = 75, n = 1050.
Substitute these values into the equation and solve for k:







Therefore, the exponential growth equation to represent the number n of cells in the dish after t minutes is:

where:
- n is the number of bacteria cells.
- t is the time (in minutes) after 1:00 PM.
To predict the number of minutes after 1:00 PM when there will be 10,000 bacteria, substitute n = 10000 into the equation and solve for t:







To calculate the time, add 142 minutes to 1:00 PM.

Therefore, the time when there will be 10,000 cells in the dish is 3:22 PM.