Aculture of yeast grows at a rate proportional to its size. if the initial population is 1000 cells and it doubles after 4 hours, answer the following questions.1)write an expression for the number of yeast cells after tt hours. p(t)=2) find the number of yeast cells after 10 hours? 3) find the rate at which the population of yeast cells is increasing at 1010 hours. answer (in cells per hour): ? ?

a)

b)

c)

Step-by-step explanation:

Part 1

For this case we assume an exponential growth model given by the following differential equation:

Where P represent the population and t the times in hours. And each 4 hours the population is doubled.

If we solve the differential equation we got:

Integrating both sides we got:

If we use exponential on both sides we got:

And for this case and we have this:

Then after 4 hours we have that the population is doubled so then would be 2000 cells and we got:

And we can solve for k like this:

So then our model is given by:

Part 2

For this case we just need to replace t= 10 hours into the model and we got:

Part 3

For this case we can find the rate like this:

lol

step-by-step explanation:

step-by-step explanation:

the original amount doesn't ''re just looking for the time it takes for 1/2 of the substance to we have

(1/2) =)     take the ln   of both sides

ln (1/2)   = )   and we can write

ln(1/2) = ) lne     and lne   = 1     so we have

ln(1/2) = -.1092t     divide both sides by -.1092

t = ln(1/2)/-.1092 = about 6.347 days = about 6.3 days (rounded)