You start with 23 billion yeast cells (23x10e9) and they have a doubling time of 90 minutes, after how long will your starter hold 90 billion yeast?
Please input your answer in minutes
x(t) = x0 × (1 + r) t
My answer is 136..
is this correct?
Thanks
check your calculations
90 = 23 * 2^(m / 90)
log(90 / 23) = (m / 90) log(2)
To determine the time it takes for the yeast cells to reach 90 billion, we can use the formula for exponential growth:
x(t) = x0 × (1 + r)^(t / d)
Where:
x(t) = final population size (90 billion yeast cells)
x0 = initial population size (23 billion yeast cells)
r = growth rate per doubling time (ln(2) / 90 minutes)
t = time in minutes
d = doubling time (90 minutes)
Using these values, we can rearrange the equation to solve for t:
(90 billion yeast cells) = (23 billion yeast cells) × (1 + ln(2) / 90)^t/90
Taking the natural logarithm of both sides:
ln(90) = ln(23) + ln(1 + ln(2) / 90)^t/90
Simplifying further:
t/90 = [ln(90) - ln(23)] / ln(1 + ln(2) / 90)
Now, we can solve for t:
t = 90 × [ln(90) - ln(23)] / ln(1 + ln(2) / 90)
Calculating this expression gives us:
t ≈ 99.16 minutes
Therefore, it will take approximately 99.16 minutes for the yeast cells to reach 90 billion. Your answer of 136 minutes is incorrect.
To solve this problem, let's use the formula for exponential growth:
N(t) = N₀ * (2^(t/d))
Where:
N(t) is the final number of yeast cells at time t
N₀ is the initial number of yeast cells
t is the time in minutes
d is the doubling time
In this case, N₀ = 23 billion (23 x 10^9) yeast cells and we want to find the time it takes for the population to reach 90 billion (90 x 10^9) yeast cells.
Let's substitute the values into the formula:
N(t) = 23 x 10^9 * (2^(t/90))
Now we can solve for t by setting N(t) equal to 90 x 10^9:
90 x 10^9 = 23 x 10^9 * (2^(t/90))
Divide both sides by 23 x 10^9:
90/23 = 2^(t/90)
Take the logarithm of both sides to isolate the exponent:
log2(90/23) = t/90
Multiply both sides by 90:
90 * log2(90/23) = t
Using a calculator, we find:
t ≈ 170.3 minutes
Therefore, it would take approximately 170.3 minutes for the yeast population to reach 90 billion cells.
Your answer of 136 minutes is not correct.
ok Sir
would be 270 minutes