The amount of bacteria after n min if the initial amount of bacteria is q and the amount of bacteria doubles every minute.

I suggest you make a table.Start with 0 time and 1 bug.

time #bugs
0&nbsp&nbsp&nbsp&nbsp&sbsp&nbsp&nbsp&nbsp1
1&nbsp&nbsp&nbsp&nbsp&sbsp&nbsp&nbsp&nbsp2
2&nbsp&nbsp&nbsp&nbsp&sbsp&nbsp&nbsp&nbsp4
3&nbsp&nbsp&nbsp&nbsp&sbsp&nbsp&nbsp&nbsp8
4&nbsp&nbsp&nbsp&nbsp&sbsp&nbsp&nbsp&nbsp16
5&nbsp&nbsp&nbsp&nbsp&sbsp&nbsp&nbsp&nbsp32

Note that 2^2 = 4 and 2^3 = 8 and 2^4 = 16. Do you see a pattern?

So, you start with q bacteria. After one minute, you it will double, so you'll have 2q bacteria. After 2 minutes, it will again double, so you'll have 4 q bacteria. AFter 3 minutes, it will again double, so you'll have 8q bacteria. After 4 minutes, it will again double, so you'll have 16q bacteria. Can you see the relationship minutes and the amount of q bacteria?

Thank you Dr. Bob and Dan!

We did go over a problem similar like this in my class - but, I did not really understand it then very well. I really dislike word problems!

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I understand that word problems can be challenging, but they're a great way to practice applying mathematical concepts to real-life situations! In this case, the relationship between the minutes (n) and the amount of q bacteria can be expressed using exponential growth:

Amount of bacteria = q * 2^n

Here, q is the initial amount of bacteria, n is the number of minutes passed, and 2^n represents the doubling of bacteria every minute. So, for any given time n minutes, you can calculate the amount of bacteria present by multiplying the initial amount by 2 raised to the power of n.

I understand that word problems can be challenging. In this case, we can use the formula for exponential growth to solve the problem. The formula is:

A = P * (1 + r)^n

Where:
A = final amount of bacteria
P = initial amount of bacteria
r = growth rate (in this case, 2 since the amount doubles every minute)
n = number of minutes

To find the amount of bacteria after n minutes, we can substitute the given values into the formula. In this case, P = q.

A = q * (1 + 2)^n
A = q * (1 + 2)^n
A = q * 2^n

So, after n minutes, the amount of bacteria will be q * 2^n.

No problem! Understanding word problems can be challenging, but breaking them down into simpler steps can help make them easier to solve. In this case, we are given that the amount of bacteria doubles every minute.

To find the amount of bacteria after a given number of minutes, you can use the formula:

Amount of bacteria = initial amount of bacteria * (doubling factor ^ number of minutes)

In this case, the initial amount of bacteria is q and the doubling factor is 2 (since the amount doubles every minute).

So, the formula becomes:

Amount of bacteria after n minutes = q * (2 ^ n)

For example, if the initial amount of bacteria is 1 (q = 1) and we want to find the amount of bacteria after 5 minutes (n = 5), we can substitute these values into the formula:

Amount of bacteria after 5 minutes = 1 * (2 ^ 5) = 1 * 32 = 32

Therefore, after 5 minutes, the amount of bacteria will be 32.

I hope this explanation helps! Let me know if you have any further questions.