Question

I am reviewing and would like to know how to do this!! The number of salmonella bacteria, y, in a sample after M minutes can be found using the equation shown. y=1,200(2^20/60*M) How many minutes will it take for the sample to have 100,000 bacteria?

Answer 1

I know the answer is 19.1 I would just like to know how they got it

Answer 2

@ganeshie8 @Luigi0210

Answer 3

They had inputted the sample of 100,000 bacteria where y was since that was the total....they then simplified down to find (m) minutes....

\(\LARGE{100,000=1,200(\frac{2^{20}}{60 \times m})}\)

Answer 4

Oh okay, see I understood that they had inputed 100,000 for y

Answer 5

Just couldnt get the m part

Answer 6

@563blackghost when you do it how you wrote it it gives you 1097985.34 not 100,000

Answer 7

Y is know as the number of salmonella bacteria...we have that information which states that there is 100,000 salmonella bacteria....but we did not get information of how many minutes it took to produce that much bacteria so we leave m alone....

Answer 8

They ask for what m would be. The answer they give is 19.1

Answer 9

@563blackghost

Answer 10

@sleepyjess @freckles @IrishBoy123 @ILovePuppiesLol

Answer 11

maybe check your formula again?

eg if you set m = 0, you get \(y = \infty\)

whilst my guess is that the bacteria are meant to grow, not die

Answer 12

The formula is written how i put it so y=1,200(2^(20/60*M))

Answer 13

@IrishBoy123

Answer 14

solving it as you state it gives \(m \approx 210\)

Answer 15

I assume your equation is
\[ y = 1200 \cdot 2^{\frac{20}{60} m }\]
which can be simplified a little , because 20/60 is ⅓:
\[ y = 1200 \cdot 2^{\frac{m}{3} }\]

to find m when y is 100,000 we replace y with 100000
\[ 100000 = 1200 \cdot 2^{\frac{m}{3} }\]
divide both sides by 1200:
\[ \frac{250}{3} = 2^{\frac{m}{3} }\]
or
\[ 2^{\frac{m}{3} } = \frac{250}{3} \]

Answer 16

to "solve for m" when m is an exponent, you should think *logarithm*
we can use either log (base 10) or ln (log base 3) (those are the ones most calculators can do)

let's use log base 10. "take the log" of both sides. that means do this:
\[ \log\left(2^{\frac{m}{3} }\right) = \log\left( \frac{250}{3} \right)\]

on the left side, we use this rule:
\[ \log(a^b) = b \log(a) \]
to "bring down" the exponent. notice that this is how we can "get at" the exponent:
\[ \frac{m}{3} \log(2) = \log\left( \frac{250}{3} \right)\]
multiply both sides by 3/log(2) (this looks complicated, but it is just a number)
we get
\[ m = \frac{3}{\log2}\log\left( \frac{250}{3} \right)\]

we will need a calculator to get the numerical value of m

Answer 17

you can also type into the google search window
3/log(2) * log(250/3)=
and the google calculator will show the answer: 19.1424653518

Answer 18

*note: ln means log base "e" not 3

Answer 19

you can use the OS draw function to enter tricky formulae