# Calculus

posted by .

A population of 500 E. coli bacteria doubles every 15 minutes. Use this information to find an expression for this population growth. Using this expression, find what the population would be in 87 minutes. Use an exponential model.

so we're supposed to use P(t)= (Po)(e)^kt

so P(o) would be 500,
and then would t be 15 or 0.25 and wowhat would k be? 2?

• Calculus -

in P(t) = 500 e^kt
it depends whether you want to to be in minutes or hours.

let's do it for minutes, then
1000 = 500 e^15k
2 = e^15k
15k = ln2
k = (ln2)/15

if you want t to be hours then use .25 for t in
1000 = 500 e^.25K
.
.
K = ln2/.25 or K = 4ln2

• Calculus -

okay, so then in 87 minutes what would it be?

• Calculus -

let's use our first one, the one in minutes
P(87) = 500 e^(87*ln2/15)
= 500 e^4.020254
= 27857.6

remember it doubles every 15 min

so after 15 min --> 1000
after 30 min ---> 2000
after 45 min ---> 4000
after 60 min ---> 8000
after 75 min ---> 16000
after 90 min ---> 32000

we could check to see if we get 32000 for 90 minutes

P(90) = 500 e^(90*ln2/15)
= 500(64) = 32000 YES!!!!

• Calculus -

whao! that makes so much sense.
just a quick question, how do u know what e is?

thanks so much
<3333333333

• Calculus -

e is one of these very strange transcendental numbers like pi

one defn of e is
1 + 1/1! + 1/2! + 1/3! + ... to infinitity

where something like 5! = 1*2*3*4*5

or
e = Limit (1 + 1/n)^n where n approaches infinitity

The Swiss/German mathematician Euler spent a lot of time with the concept of that number and e is often called Euler's number

• Calculus -

e is approximately 2.71828

## Similar Questions

1. ### Calculus

Suppose that a population of bacteria triples every hour and starts with 700 bacteria. (a) Find an expression for the number n of bacteria after t hours. n(t) = ?
2. ### Calc

The number of bacteria in a culture is increasing according to the law of exponential growth. There are 125 bacteria in the culture after 2 hours and 350 bacteria after 4 hours. a) Find the initial population. b) Write an exponential …
3. ### Math

The size of a bacteria population is given by P=C*e^(kt) Where C is the initial size of the population, k is the growth rate constant and t is time in minutes. a) If the bacteria in the population double their number every minute, …
4. ### Calculus

The growth rate of Escherichia coli, a common bacterium found in the human intestine, is proportional to its size. Under ideal laboratory conditions, when this bacterium is grown in a nutrient broth medium, the number of cells in a …
5. ### Algebra

Under ideal conditions, a population of e. coli bacteria can double every 20 minutes. This behavior can be modeled by the exponential function: N(t)=N(lower case 0)(2^0.05t) If the initial number of e. coli bacteria is 5, how many …
6. ### pre-calculus

Assume that the number of bacteria follows an exponential growth model: P(t)=P0ekt . The count in the bacteria culture was 900 after 20 minutes and 1600 after 30 minutes. (a) What was the initial size of the culture?
7. ### Algebra

Suppose that the number of bacteria in a certain population increases according to a continuous exponential growth model. A sample of 1000 bacteria selected from this population reached the size of 1274 bacteria in five hours. Find …
8. ### Math

The population of bacteria in a petri dish doubles every 12 h. The population of the bacteria is initially 500 organisms. How long will it take for the population of the bacteria to reach 800?
9. ### Math/Pre-calculus

Assume that the number of bacteria follows an exponential growth model: P(t)=P0e^k/t. The count in the bacteria culture was 400 after 10 minutes and 1500 after 35 minutes. (a) What was the initial size of the culture?
10. ### Algebra

Suppose that the number of bacteria in a certain population increases according to a continuous exponential growth model. A sample of 1800 bacteria selected from this population reached the size of 2272 bacteria in five hours. Find …

More Similar Questions