# Calculus

posted by .

a populatioin of bacteria has an initial size of 500. the population doubles every 7 hours.
a) how many bacteria will there be after 10 hours
b) when will there be 3000 bacter?

I keep getting answers that just don't make sense. Can someone do these out for me......its practice, not homework. I have a test tomorrow.

• Calculus -

I would set my equation as

N = 500(2)^(t/7) , where 7 is the number of hours

a)when t=10
N = 500(2)^(10/7) = 1345.9 or 1346 bacteria

b) set 3000 = 500(2)^(t/7)
6 = 2^(t/7)
t/7 = log6/log2
t = 7log6/log2 = 18.1

makes sense ....
after 7 hours 1000
after 14 hours 2000
after 21 hours 4000 , 3000 seems reasonable after 18

• Calculus -

sorry I forgot to mention I have to use the equation: p(t)= ce^kt

• Calculus -

ok, then change it to

N = 500(e)^(kt)
when t = 7
1000 = 500(e)^(7k)
2 = (e)^(7k)
7k = ln2
k = ln2/7 = .09902

N = 500(e)^(.09902t)

now follow the same steps as before
a) let t=10 .... ( I got exactly the same answer as before)

## Similar Questions

1. ### calculus

a bacteria pop. grows exponentially. There are 1500 bacteria after 3 hours and 20,000 after 8 hours. ahving trouble finding the initial bacteria pop. thanks for the help In five hours the population get's larger by a factor 13 + 1/3-----> …
2. ### 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) = ?
3. ### Precalculus

NEED HELP ASAP PLEASE!! A bacteria culture starts with 2000 bacteria and the population doubles every 3 hours. a) A function that models the number of bacteria after t hours is p(t)=____________?
4. ### precalculus

A bacteria culture initially contains 1500 bacteria and doubles every half hour. a) Find an expression for the number of bacteria after t hours. Q(t)= b) The number of bacteria after 20 minutes is (the answer must be an integer) c) …
5. ### calculus

A bacteria culture starts with 900 bacteria and the population doubles every 4 hours. Find an expression for the number of bacteria after t hours.
6. ### 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 …
7. ### math

The number of bacteria in a culture is modeled by n(t)=1710e071t (a) The initial number of bacteria is (b) The relative rate of growth of this bacterium population is (c) The number of bacteria after 3 hours is (d) After how many hours …
8. ### Math

he number of bacteria in a culture is modeled by n(t)=1710e071t (a) The initial number of bacteria is (b) The relative rate of growth of this bacterium population is (c) The number of bacteria after 3 hours is (d) After how many hours …
9. ### CALCULUS

a bacteria culture grows with a constant per capita growth rate. After 2 hours there are 500 bacteria and after 6 hours the count is 312500, find the initial population and the population after 8 hours
10. ### algebra

In an experiment, the population P of bacteria is given by P=1000e^kt,where k is constant.If the size of population bacteria is found to be 3000 after 10 hours, what is the size of the population after 5 hours?

More Similar Questions