# Calculus

posted by .

A bacteria culture contains 200 cells initially and grows at a rate proportional to its size. After half an hour the population has increased to 360 cells.
(a) Find the number of bacteria after t hours.
(b) Find the number of bacteria after 4 hours.
I found part a, P(t)= 200e^(1.2*t)
but when I solve part b it's different than the model answer!

• Calculus -

I found the following:
360 = 200 e^(.5k) , where k is a constant
1.8 = e^(.5k)
ln 1.8 = .5k lne
.5k = ln 1.8
k = 1.1755733..

so Number = 200 e^(1.755733t)
when t=4
number = 200 e^4.702293..
= 22039.9
or appr 22040 bacteria

It looks like you rounded of the value of k too early.
Since you are using a calculator anyway, why round off any numbers at all ?
Just use them the way they appear on your device, so there is no need to re-enter any numbers.
I also use the memory locations of my calculators to store any intermediate results.
If we use your value of k = 1.2
Number = 200 e^(4*1.2) = appr 24302 which is significantly different from the answer I got.

## Similar Questions

1. ### math

A bacteria culture starts with 260 bacteria and grows at a rate proportional to its size. After 4 hours there will be 1040 bacteria. (a) Express the population after t hours as a function of t. this is what i put as my answer but i …
2. ### 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) …
3. ### MATH :)

3. In Biology, it is found that the bacteria in a certain culture double every half-hour. If the initial number of bacteria in culture is 1000, A. Find the defining equation for the number N of bacteria in culture after T hours, assuming …
4. ### 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
5. ### maths --plse help me..

A bacteria culture has an initial population of 600. After 4 hours the population has grown to 1200. Assuming the culture grows at a rate proportional to the size of the population, find the function representing the population size …
6. ### Calculus (math)

A bacteria culture grows with constant relative growth rate. The bacteria count was 784 after 2 hours and 117649 after 6 hours. What is the relative growth rate?
7. ### Urgent math

The initial size of a culture of bacteria is 1000. After one hour the bacteria count is 4000. (a) Find a function n(t) = n0ert that models the population after t hours. n(t) = b)Find the population after 1.5 hours. (Round your answer …
8. ### Algebra

At noon, Professor Simon has a petri dish with 10,000 cells of Bacteria A. In another petri dish, he has 33,000 cells of Bacteria B. Every hour, Bacteria A grows by 8%. Every hour Bacteria B cells die off, decreasing the number of …