What is the answer and explain please.?

Question

A bacteria culture grows with a constant relative growth rate. After 14 hours there are 1000 bacteria and after 20 hours there are 70000 bacteria.
a)Find the initial population.
b)Find an expression for the population after t hours.
c)Find the number of cells after 17 hours.
d)Find the rate growth after 17 hours.
e)When will the population reach 155000 bacteria?
f)Find an expression for the population after t hours.
g)Find the number of cells after 17 hours.
h)Find the rate growth after 17 hours.


When will the population reach 155000 bacteria?

Answer 1

P(t)=Ae^(kt)

A is the initial population and k is the growth rate

1000=Ae^(k*14) (I)

70000=Ae^(k*20) (II)

first find k by dividing equation II by equation I

we get

70=e^(20k-14k)=e^6k

take the ln of both sides we get k=0.7081

using this value of k go back to equation one and find A

1000=Ae^(.7081*14)

A=.0495

so P(t)=.0495*e^(.7081t)

at 17 hours we should have .0495*e^(.7081*17)=8366

if P(t)=155000=.0495e^(.7081t)

solve for t, you'll get t=21.1 hrs.

Answer 2

Use the exponential growth function, formula (1) on this page is the only formula you need to use I think:

http://mathworld.wolfram.com/ExponentialGrowth.html

Answer 3

N = N0*e^(t/tau)

You use the ratio of the two data points to get you tau. Then you can use either datapoint to solve for N0.