A culture of bacteria grows exponentially. It doubles in size every 16 hours. How long will it take to triple from its original size?

3 = 1(2)^(t/16)

log 3 = log 2^(t/16)
log 3 = (t/16)log 2
t/16 = log3/log2
t = 16(log3/log2) = 25.36 hours

Well, let's see here. If the bacteria doubles in size every 16 hours, then it's safe to assume that after 16 hours, it is twice its original size. But what happens after that? Triple the size you say? That's a tall order for our little bacteria buddies!

So, if they double in size every 16 hours, it will take another 16 hours for them to double again, bringing us to 32 hours in total. But wait, they need to triple in size, not just double. So, let's do some more math magic!

If they double in size every 16 hours, and we're already at 32 hours now, then it would take another 16 hours for them to double again. But this time, instead of just getting double, they'll get tripled! So we add on another 16 hours, making it a total of 48 hours.

So, my friend, it will take 48 hours for our bacterial buddies to triple in size from their original size. Just remember, exponential growth can be a real jokester sometimes!

To find out how long it will take for the bacteria to triple from its original size, we can use the formula for exponential growth. The formula is:

N = N0 * 2^(t / t_double)

Where:
- N is the final population size
- N0 is the initial population size
- t is the time period in hours
- t_double is the time it takes for the population to double

In this case, we want to find the time it takes to triple the population, so N = 3 * N0. Let's substitute this into the formula:

3 * N0 = N0 * 2^(t / t_double)

Now we can simplify the equation and solve for t:

2^(t / t_double) = 3
Taking the logarithm on both sides:
t / t_double = log2(3)
t = log2(3) * t_double

We know that the bacteria double in size every 16 hours, so t_double = 16. Let's calculate the value of t:

t = log2(3) * 16 ≈ 24.44

Therefore, it will take approximately 24.44 hours to triple in size.

To find out how long it will take for the bacteria culture to triple in size, we need to determine the number of doubling periods that are required.

Since the bacteria doubles in size every 16 hours, we can express this growth using the formula:

N = N₀ * 2^(t / 16)

Where:
N = Final size of the bacteria culture
N₀ = Initial size of the bacteria culture
t = Time in hours

Since we want to triple the initial size, the final size would be 3 times the initial size, so we can write the equation as:

3N₀ = N₀ * 2^(t / 16)

Canceling out N₀, we get:

3 = 2^(t / 16)

To solve for t, we can take the logarithm of both sides:

log base 2 (3) = t / 16

Now we can solve for t:

t = 16 * log base 2 (3)

Using a calculator, we find that log base 2 (3) is approximately 1.585.

t ≈ 16 * 1.585
t ≈ 25.36

Therefore, it will take approximately 25.36 hours for the bacteria culture to triple from its original size.