Is 12 × –1 positive or negative? positive negative Submit
1 answer:
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Answer:
- 700 initial cells
- 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.
