after the yeast population has doubled to 46 billion yeast cells, a green mold attacks your sourdough starter. This causes the yeast population to start dying by half every 2 hours.
How long would it be until there is just 1 yeast cell left? Please input your answer in hours with 2 decimal points.
Could you help me please
4.6*10^10(1/2)^(t/2) = 1 , where t is the number of hours
(1/2)^(t/2) = 1/(4.6*10^10)
(t/2) log .5 = log (1/(4.6*10^109))
t/2 = log (1/(4.6*10^109)) / log .5 = 35.4209
t = appr 70.84 hours
Well, my dear bread-making friend, I would be delighted to help you with this yeast-y dilemma. Let's crunch some numbers and add a dash of humor while we're at it!
So, the yeast population starts at 46 billion cells. And if the population is halving every 2 hours due to the attack of the green mold, we need to find out how long it would take for the yeast population to dwindle down to just one cell.
Now, to calculate the time it takes, we need to find out how many times the population halves before reaching 1 cell. Each time the population halves, we're essentially dividing it by 2.
So, if 46 billion cells halve to 1 cell, that means we need to divide by 2 a certain number of times. Mathematically speaking, we can express it as:
46 billion / 2^n = 1
Solving this equation for 'n' (the number of times the population halves) will give us the answer we seek. Let me grab my trusty calculator... wait, where did that chicken go? Hmm, never mind.
After some quick calculations, and a sprinkle of silliness, it appears that 'n' is equal to 35.64. Now, we can't have half a population, so we can round up to 36 times.
Since each halving takes 2 hours, we multiply 36 by 2 to find the total time it takes for the population to reach just 1 cell. And Voila! The answer is 72 hours, or 3 days!
So, my friend, you better protect your sourdough starter from green mold invasions and preserve those yeast cells. May your bread always be fluffy and delicious, even with a touch of moldy humor thrown in!
Sure! I can help you calculate the time until there is just 1 yeast cell left.
Since the yeast population starts with 46 billion cells and halves every 2 hours, we can use the following formula to calculate the time it takes for the population to reach 1 cell:
N = (N0 / 2)^(t / 2)
Where:
N = Number of yeast cells at time t,
N0 = Initial number of yeast cells (46 billion),
t = Time in hours.
We want to solve for t when N equals 1. Let's set up the equation:
1 = (46 billion / 2)^(t / 2)
To solve this equation, we need to take the logarithm of both sides. In this case, we can use the natural logarithm (ln) since it will result in a more manageable expression:
ln(1) = ln((46 billion / 2)^(t / 2))
Simplifying further:
0 = (t / 2) * ln(23 billion)
Now, divide both sides of the equation by ln(23 billion) to solve for t:
t / 2 = 0 / ln(23 billion)
t = 0
Hence, the time it takes for the yeast population to reach 1 cell is 0 hours.
Of course! To find out how long it would take for the yeast population to decrease to just 1 yeast cell, we can use exponential decay.
Let's break down the information we have:
Initial yeast population: 46 billion yeast cells
Yeast population reduces by half every 2 hours
To solve this problem, we can use the formula for exponential decay:
N(t) = N0 * (1/2)^(t/h)
Where:
N(t) is the final population size we want to find (1 yeast cell)
N0 is the initial population size (46 billion yeast cells)
t is the time it takes for the population to reach N(t) (unknown)
h is the time it takes for the population to decrease by half (2 hours)
Plugging in the values, we have:
1 = 46,000,000,000 * (1/2)^(t/2)
To solve for t, we need to isolate it on one side of the equation. Let's take the logarithm (base 2) of both sides to simplify it:
log2(1) = log2(46,000,000,000 * (1/2)^(t/2))
0 = log2(46,000,000,000) + log2(1/2)^(t/2)
Since log2(1/2) = -1, we can substitute it into the equation:
0 = log2(46,000,000,000) + (-1)^(t/2)
Now we isolate t/2:
- log2(46,000,000,000) = (t/2)
Finally, solving for t:
t = 2 * (- log2(46,000,000,000))
t ≈ 89.86
So it would take approximately 89.86 hours for the yeast population to decrease to just 1 yeast cell.