if there are initial 2500 bacteria in a culture, and the number of bacteria double each hour, the number of bacteria after t hours cab n be found using the formula=N=2500(2^t).how long will it take the culture to grow to 75,000 bacteria.
75000=2500(2)^t
take the log of each side:
log(75000)=log(2500)+tlog(2)
log(30)=t log (2)
t= log(30)/log(2)
solve for t. Your calculator is your best friend on this. I get about five hours
Oh, bacteria sure know how to party! Let's calculate the time it takes for them to hit 75,000. We have the formula N = 2500(2^t). Given that N = 75,000, we can set up the equation like this:
75,000 = 2500(2^t)
Now, to solve for t, we need to apply some math magic. First, let's divide both sides by 2500:
30 = 2^t
Next, we need to isolate t by taking the logarithm of both sides. Shall we say, the bacterial logarithm?
log 30 = log (2^t)
Using the power rule of logarithms, we can bring down the exponent:
log 30 = t log 2
Now we divide both sides of the equation by log 2:
t = log 30 / log 2
Plugging this into a calculator, we find that t is approximately 4.9 hours.
So, after approximately 4.9 hours, that culture will have a bacterial population of 75,000. Those bacteria sure like to multiply, don't they? It's like they never learned about the birds and the bees!
To find out how long it will take for the culture to grow to 75,000 bacteria, we can use the given formula N = 2500(2^t), where N represents the number of bacteria after t hours.
Let's solve for t:
N = 2500(2^t)
We want to find t when N is equal to 75,000:
75,000 = 2500(2^t)
Divide both sides of the equation by 2500:
75,000/2500 = 2^t
Simplify the left side:
30 = 2^t
To determine the value of t, we need to find the exponent that results in 2^t equaling 30.
Since 2^5 equals 32, and 2^4 equals 16, we know that t must be greater than 4 and less than 5.
Now, we can estimate the value of t:
2^4 = 16
2^4.5 is approximately 22.63
2^5 = 32
So, t is between 4.5 and 5.
To get a more precise value of t, we can use logarithms:
log(base 2) of (30) = t
Using a calculator or logarithm tables, we find:
t ≈ 4.9069
So, it will take approximately 4.9069 hours (or about 4 hours and 55 minutes) for the culture to reach 75,000 bacteria.