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
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
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!
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.