Question

Phillipa is a scientist who grows yeast cells. She starts her experiment with 700 yeast cells and notices the growth rate of the cells is 5.2%.

#1 How many yeast cells are there when Phillipa starts her experiment?

#2 Find the number of yeast cells present after 25 hours.

Sketch a graph that represents the situation.

As part of a complete answer, be sure to:
a. Label your x- and y-axis with a title, units, and intervals.
b. Mark and label the coordinate point of your answer in question #1.
c. Mark and label the coordinate point of your answer in question #2.

Answer 1

Answer:

1. 700 initial cells
2. 2486 cells after 25 hours

Step-by-step explanation:

#1 There are 700 yeast cells when Phillipa starts her experiment. (This value is given in the problem statement.)

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#2 For this, we must assume the time period that is associated with the 5.2% growth. (The problem statement does not specify it.)

The general form of the equation for exponential growth is ...

  f(t) = (initial value)×(growth multiplier in time period)^(number of periods)

When the growth (or decay) rate is indicated as a percentage (r), the "growth multiplier in time period" is generally ...

  growth multiplier = 1+r

Here, the value of "r" is 5.2% = 0.052, so the growth multiplier in the time period is ...

  1 + 0.052 = 1.052

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As we said, the time period is not specified. Since the only time period mentioned in the problem is 25 hours, we might reasonably assume that the 5.2% growth occurs in one hour. Then the cell population is ...

  f(t) = 700×1.052^t . . . . . . for t in hours

After 25 hours, ...

  f(25) = 700×1.052^25 ≈ 700×3.55135 ≈ 2485.9 ≈ 2486

The number of yeast cells present after 25 hours is about 2486.