A certain strain of bacteria divides every four hours. If a colony is started with 10 bacteria, then the time t (in hours) required for the colony to grow to N bacteria is given by
t = 4(log(N/10)/log2
Find the time required for the colony to grow to one million bacteria. (Round your answer to two decimal places.)
N=1000000
you plug this number into the equation like shown below
4(log(1000000/10))/log(2)
log(1000000/10)=5
log(2)=.301029
4(5/.301029)=66.4387
the answer is 66.44 if you round it to two decimal places.
I hope this helps :)))
Thank you!!!
Why did the bacteria go to school? Because they wanted to multiply their knowledge!
Now let's solve the problem.
Given that the time required for the colony to grow to N bacteria is given by:
t = 4(log(N/10)/log2)
We want to find the time required for the colony to grow to one million bacteria (N = 1,000,000).
Plugging in N = 1,000,000 into the equation, we have:
t = 4(log(1,000,000/10)/log2)
First, let's simplify the logarithmic expression:
log(1,000,000/10) = log(100,000) = 5
Now we can substitute it back into the equation:
t = 4(5/log2)
Using a calculator, we find that log2 is approximately 0.69314.
t ≈ 4(5/0.69314)
t ≈ 4(7.213)
t ≈ 28.85
So, the time required for the colony to grow to one million bacteria is approximately 28.85 hours.
To find the time required for the colony to grow to one million bacteria, we need to substitute N = 1,000,000 into the equation for t.
t = 4(log(N/10)/log2)
t = 4(log(1,000,000/10)/log2)
First, we simplify the expression inside the logarithm:
log(1,000,000/10) = log(100,000) = 5
Now we substitute this value back into the equation for t:
t = 4(5/log2)
To calculate t, we need to evaluate log2. We can use a calculator to find that log2 is approximately 0.693.
t = 4(5/0.693)
t = 20/0.693
t ≈ 28.81
Therefore, the time required for the colony to grow to one million bacteria is approximately 28.81 hours.
To find the time required for the colony to grow to one million bacteria, you can substitute the value of N = 1 million into the given equation:
t = 4(log(N/10)/log2)
t = 4(log(1,000,000/10)/log2)
Before we proceed, let's simplify the expression inside the logarithm:
log(1,000,000/10) = log(100,000)
Using the property of logarithms, we can rewrite this as:
log(100,000) = log(10^5)
Since the log of a number raised to a power is equal to the power times the log of the number, we get:
log(10^5) = 5 * log(10)
Now, we know that the logarithm of 10 with base 10 is equal to 1, so we can simplify further:
5 * log(10) = 5 * 1 = 5
Finally, we substitute this simplified value back into the equation:
t = 4(log(N/10)/log2) = 4(5/log2) = 20/log2
Using a calculator, we can evaluate this expression:
t ≈ 20/log2 ≈ 20/0.6931 ≈ 28.85
So, the time required for the colony to grow to one million bacteria is approximately 28.85 hours (rounded to two decimal places).