A bacteria culture doubles in size every 3 hours If the bact

A bacteria culture doubles in size every 3 hours. If the bacteria population is initially 2000 bacteria, find an exponential function that describes the number of bacteria that will be present after t hours. Find the number of bacteria that will be present after 5 hours. When will the bacteria population reach 6500 bacteria? Suppose that $ 10,000 is invested at an interest rate of 5.2% per year, compounded continuously. Find an exponential function that describes the amount in the account after time t, in years. What is the balance after 2 years? What is the doubling time? How old is a skeleton that has lost 27% of its carbon-14? (Remember that the radioactive element carbon-14 has a half life of 5750 years.)

Solution

22.

Bacteria doubles in every 3hrs

Exponential model for growth :N(t) = Noe^(kt)

find grwoth constant k: 2 No = Noe^(2k)

k = ln2/2 = 0.347

Intially , No = 2000 bacteria

a) Equation for growth :

N (t) = 2000e^(0.347t)

b) After 5 hrs no. of bacterias:

N(5) = 2000e^(0.347*5) = 2000*5.67 = 11340 bacterias

c) N(t) = 6500 bacterias

6500 = 2000e^(0.347t)

take natural log on both sides:

ln( 6500/2000) = 0.347t

t = 3.39 hrs