#1

Okay so I have a question on a math lab and I have no clue how to even go about starting it.

In an optimal environment, a bacteria population grows exponentially. At noon

in the sewage treatment plant, experimenters introduce specially cultured bacteria

into a barrel full of rich nutrients. We will assume that the bacteria population in

the barrel is modeled by an exponential function.

Let N(t) be the number of bacteria after t days. Then N(t) = Pa^t for some

constants P and a. Measurements indicate that N(2) = 5, 400 and N(6) = 345, 000.

(a) Before working the problem, estimate (guess!) the value of N(4), the number

of bacteria at noon on the fourth day.

(b) Write down two equations for P and a, one when t = 2 and the other when

t = 6.

(c) Use these two equations to compute a and P. Round your values to three

signiﬁcant digits, but be sure to store the more precise values for further cal-

culations.

So where I'm confused is that I don't know how to get two values from an equation with two variables. And I'm not trying to get the pit to do my homework. I'm not even asking for the answer. I just need a push in the right direction.

In an optimal environment, a bacteria population grows exponentially. At noon

in the sewage treatment plant, experimenters introduce specially cultured bacteria

into a barrel full of rich nutrients. We will assume that the bacteria population in

the barrel is modeled by an exponential function.

Let N(t) be the number of bacteria after t days. Then N(t) = Pa^t for some

constants P and a. Measurements indicate that N(2) = 5, 400 and N(6) = 345, 000.

(a) Before working the problem, estimate (guess!) the value of N(4), the number

of bacteria at noon on the fourth day.

(b) Write down two equations for P and a, one when t = 2 and the other when

t = 6.

(c) Use these two equations to compute a and P. Round your values to three

signiﬁcant digits, but be sure to store the more precise values for further cal-

culations.

So where I'm confused is that I don't know how to get two values from an equation with two variables. And I'm not trying to get the pit to do my homework. I'm not even asking for the answer. I just need a push in the right direction.

#2

So where I'm confused is that I don't know how to get two values from an equation with two variables. And I'm not trying to get the pit to do my homework. I'm not even asking for the answer. I just need a push in the right direction.

Make one variable a function of the other, then solve for that one. Then you can substitute that value in and solve for the other.

#3

there is a specific thread for homework questions

#4

I used to know how to do this. My mind is shot. :/ Sorry.

#5

Everything equals Jesus.

#6

N(2) = 5, 400

and

N(t) = Pa^t

so...

N(2) = Pa^2

and

5400 = Pa^2

Following

345, 000 = Pa^6

.

Now you should easily know what to do. Move one of the equations around so that you get P = ???. and just substitute ??? where the P is in the other equation.

and

N(t) = Pa^t

so...

N(2) = Pa^2

and

5400 = Pa^2

Following

345, 000 = Pa^6

.

Now you should easily know what to do. Move one of the equations around so that you get P = ???. and just substitute ??? where the P is in the other equation.

#7

you will have to think a little bit about part a, but part b and c are easy (well for me). for b, you just plug in the values of t into N(t). because you have an N value for them both, you plug that in too. so you have:

5400=P(a^2) and 345000=P(a^6)

solve one for P and plug it into the other. In other words:

P=(5400)/(a^2)

Plug that into the other one and solve for a. Then use that value to solve for P by plugging into one of the three equations (i would use the third one since you already have P solved for).

for the rest of part b, just solve for a.

Hope this helps. Any more algebra/calculus problems, feel free to PM me.

5400=P(a^2) and 345000=P(a^6)

solve one for P and plug it into the other. In other words:

P=(5400)/(a^2)

Plug that into the other one and solve for a. Then use that value to solve for P by plugging into one of the three equations (i would use the third one since you already have P solved for).

for the rest of part b, just solve for a.

Hope this helps. Any more algebra/calculus problems, feel free to PM me.

#8

Thanks guys. And JKM i might need to haha. I suck at math.

#9

Thanks guys. And JKM i might need to haha. I suck at math.

https://www.ultimate-guitar.com/forum/showthread.php?t=658547&highlight=math%2Fscience

For future reference.

#10

Thanks guys. And JKM i might need to haha. I suck at math.

well math is my specialty. i'm in calculus 3 and physics 1 currently, and will be in differential equations and physics 2 next semester. any math problems you have, i'll be glad to help.

or you can refer to that thread above...either route should yield the same results.

good luck.

*Last edited by JKMV11 at Oct 25, 2009,*