I not sure I have enough information or if I'm using the correct formula, help?

[jazz]

Nic was growing a culture of bacteria for a biology experiment. He noticed that the population doubled after 90 minutes. If the population grows exponentially, how many times the original population will there be after six hours?

I put this into bg^t
I had b as 1
I had g as 2
I had ^t as 6

My first problem I had was, do I have to convert the 6 hours to minutes or do I have to simply work this out? When I did I ended up with 820 bacteria which didn't seem right. I asked my partner in class and she said she got 1 but I can't figure out how with this type of equation she was able to get 1. Could someone help me

 

[Deleted member 4993]

Nic was growing a culture of bacteria for a biology experiment. He noticed that the population doubled after 90 minutes. If the population grows exponentially, how many times the original population will there be after six hours?

I put this into bg^t
I had b as 1
I had g as 2
I had ^t as 6

My first problem I had was, do I have to convert the 6 hours to minutes or do I have to simply work this out? When I did I ended up with 820 bacteria which didn't seem right. I asked my partner in class and she said she got 1 but I can't figure out how with this type of equation she was able to get 1. Could someone help me

Let's think through this....

In 90 minutes P became (P * 2 = ) 2P

In next 90 minutes (90+90=180 minutes total) 2P became (2P * 2 =) 4P (=2²P)

In next 90 minutes (90+90+90 = 270 minutes total) 4P became (4P * 2 =) 8P (= 2³P)

In next 90 minutes (90+90+90+90 = 360 minutes = 6hours total) 8P became (8P * 2 =) 16P (= 2⁴P)

So after 6 hours the population would 16 times that of the original population.

 

[jazz]

Core Standards? Core confusing!

Nic was growing a culture of bacteria for a biology experiment. He noticed that the population doubled after 90 minutes. If the population grows exponentially, how many times the original population will there be after six hours?

I put this into bg^t
I had b as 1
I had g as 2
I had ^t as 6

My first problem I had was, do I have to convert the 6 hours to minutes or do I have to simply work this out? When I did I ended up with 820 bacteria which didn't seem right. I asked my partner in class and she said she got 1 but I can't figure out how with this type of equation she was able to get 1. Could someone help me

Thanks. I was using the wrong formula. I didn't think time 90 minutes was part of the base population. This was confusing and I'm still not sure what formula was used. Was it just doubling the 90 minute time and not really dealing with the actual population. That assumes that the population when it started was unknown is that correct? This core standard junk is really crazy.

 

[Deleted member 4993]

That assumes that the population when it started was unknown is that correct? Yes

It could be any number greater than zero. It could be 42 or 527 or 723 or 1/2 or 1/3.

In case of something like a bacteria - the population should be an integer.

In cases like partial pressure of a gas - it (the initial value) can be a fraction (but always positive).

 

[soroban]

Hello, jazz!

Nic was growing a culture of bacteria for a biology experiment.
He noticed that the population doubled after 90 minutes.
If the population grows exponentially,
how many times the original population will there be after 6 hours?

Here's my solution . . .


The general formula is: .\(\displaystyle P \;=\;P_o\!\cdot\!2^{at}\)

. . where \(\displaystyle \begin{Bmatrix}P & =& \text{population at time }t \\ P_o &=& \text{original population} \\ a &=& \text{a constant} \end{Bmatrix}\)


The population doubles in 90 minutes.
. . When \(\displaystyle t = 90,\ = 2P_o\)

The equation becomes: .\(\displaystyle 2P_o \:=\_o\!\cdot\!2^{90a} \)

. . . . \(\displaystyle 2 \,=\,2^{90a} \quad\Rightarrow\quad 90a \,=\,1 \quad\Rightarrow\quad a \,=\,\frac{1}{90}\)

Hence, the formula is: .\(\displaystyle P \:=\_o\!\cdot\!2^{\frac{1}{90}t}\)


After 6 hours \(\displaystyle (t = 360)\), we have:

. . \(\displaystyle P \:=\_o\!\cdot\!2^{\frac{1}{90}(360)} \quad\Rightarrow\quad P \:=\_o\!\cdot\!2^4 \quad\Rightarrow\quad P \:=\:16\,P_o\)


The population will be sixteen times the original population.

(You see, we don't need to know the original population, P_o.)