Yeast growth Consider a colony of yeast ...

Question

Yeast growth Consider a colony of yeast cells that has the shape of a cylinder. As the number of yeast cells increases, the cross-sectional area A (in mm²) of the colony increases but the height of the colony remains constant. If the colony starts from a single cell, the number of yeast cells (in millions) is approximated by the linear function N(A) - CₛA, where the constant Cₛ is known as the cell-surface coefficient. Use the given information to determine the cell-surface coefficient for each of the following colonies of yeast cells, and find the number of yeast cells in the colony when the cross-sectional area A reaches 150 mm². (Source: Letters in Applied Microbiology, 594, 59, 2014)
The scientific name of baker’s or brewer’s yeast (used in making bread, wine, and beer) is Saccharomyces cerevisiae. When the cross-sectional area of a colony of this yeast reaches 100 mm², there are 571 million yeast cells.

The scientific name of baker’s or brewer’s yeast (used in making bread, wine, and beer) is Saccharomyces cerevisiae. When the cross-sectional area of a colony of this yeast reaches 100 mm², there are 571 million yeast cells.

Accepted Answer

Welcome back everyone. This problem is about yeast colonies. Yeast colonies can be considered cylinders of a constant height. The number of yeast cells in a colony can be calculated using the linear function n of a equals c s a, where the constant c s is the cell surface coefficient and a is the cross sectional area of the colony. Debarriomyces fabriae is a yeast commonly found in all types of cheese, and we want to determine the value of the cell surface coefficient for a colony of this yeast with a cross sectional area of 50 square millimeters containing 260 multiplied by 10 to the power of 6 yeast cells. We also want to calculate the number of yeast cells in the colony with a cross sectional area of 100 square millimeters. Now for our answer choices, a says that the cell surface coefficient is 9.8 multiplied by 10 to the power of 6 yeast cells per square millimeter, and the number of yeast cells in the colony is 23 multiplied by 10 to the 6 yeast cells. B says that the cell surface coefficient is 3.5 multiplied by 10 to the power of 6 yeast cells per square millimeter, and the number of yeast cells in the colony is 73 multiplied by 10 to the power of 6. C says that the cell surface coefficient is 1.3 multiplied by 10 to the power of 6 yeast cells per square millimeter, and the number of yeast cells is 130 multiplied by 10 to the 6. And d says that the cell surface coefficient is 5.2 multiplied by 10 to the power of 6 yeast cells per square millimeter, and the number of yeast cells in the colony is 5120 multiplied by 10 to the power of 6. Now, what are we trying to figure out here? Let's start with the first part of the problem which asks us to determine the value of the cell surface coefficient for of the yeast with a cross sectional area of 50 square millimeters containing 260 multiplied by 10 to the power of 6 yeast cells. Now, we already know that so here, we're trying to find let me write that properly. Determining the cell surface cell surface coefficient. We already know that the number of yeast cells equals the coefficient multiplied by the cross sectional area of the colony. From our question or from our information here, we're told that the cross sectional area is 50 square milliliters, and the number of yeast cells is 260 multiplied by 10 to the power of 6. So since we have the number of yeast cells and the cross sectional area, we can substitute in our formula to solve for the cell surface coefficient. So given the area is 50 square millimeters and the number of cells in the colony is 260 multiplied by 10 to the power of 6. Then, in our equation, it now becomes 260 multiplied by 10 to the power of 6 equals the cell surface coefficient multiplied by 50 square millimeters. If we do some transposition here, divide both sides by 50 square millimeters, that means the cell surface coefficient equals 260 multiplied by 10 to the power of 6th yeast cells divided by 50 square millimeters. And, when we work that out, we find that the cell surface coefficient equals 5.2 multiplied by 10 to the power of 6 yeast cells per square millimeter. So we've solved the first part of our problem. Let's move on to the second part. Because in the second part, it says that we want to calculate the number of yeast cells in the colony with a cross sectional area of 100 square millimeters. Now, what do we know from that part of the problem? Let's say, this is part 2. Now, that tells us that now, the cross sectional area is 100 square millimeters. So determining the number of cell yeast cells in the colony, n of a, we are given the area being 100 square millimeters. And, from our previous question, we already know that the cell surface coefficient, since it's a constant, it will be the same value. So, that means the cell surface coefficient will also be equal to 5.2 multiplied by 10 to the power of 6 yeast cells per millimeter squared or squared millimeter. Then, we can use that information to solve for the number of yeast cells in the colony. Because remember, it's equal to the cell surface coefficient multiplied by a. So again, substituting those values, that would be 5.2 multiplied by 10 to the power of 6 yeast cells per minute, multiplied by 100 square millimeters. And when we let me write the units. Very important here. So that's yeast cells per square millimeter multiplied by 100 square millimeters. And when we multiply those, when you put that into your calculator, you'll find that you'll get the number of yeast cells in the colony to be equal to 520 multiplied by 10 to the power of 6 yeast cells. So that would be our value for the number of yeast cells in the colony in part 2 and the cell surface coefficient in part 1. And when we look at both our answers, those correspond with answer choice d. Thanks a lot for watching everyone. I hope this video helped.

Key Concepts

Linear Functions

Cell-Surface Coefficient (Cs)

Cross-Sectional Area

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