SOLUTION: Bacteria are growing exponentially in an environment of unlimited space and food. The doubling time is 1 hour. a) If there are initially x milligrams of bacteria, express the ma

Question 613103: Bacteria are growing exponentially in an environment of unlimited space and food. The doubling time is 1 hour.
a) If there are initially x milligrams of bacteria, express the mass of the bacteria as a function of time t.
f(t)=
b) Use your answer to (a) to write down an equation whose solution is the time at which there are 3x milligrams of bacteria. Enter your answer in the form, eg .
c) Solve your equation from (b)
t = hours
d) Your answer to (c) should be between 1 and 2 hours. Check that it is. Do you understand why it has to be ?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Bacteria are growing exponentially in an environment of unlimited space and food. The doubling time is 1 hour.
a) If there are initially x milligrams of bacteria, express the mass of the bacteria as a function of time t.
f(t)=x*2^t
-------------
b) Use your answer to (a) to write down an equation whose solution is the time at which there are 3x milligrams of bacteria. Enter your answer in the form,
3x = x*2^t
2^t = 3
t = ln(3)/ln(2) = 1.585 hrs
--------------------------------
.
c) Solve your equation from (b)
t = 1.585 hours
-------------------------
d) Your answer to (c) should be between 1 and 2 hours. Check that it is. Do you understand why it has to be ?
The quantity is 2x after 1 hr.
The quantity is 4x after 2 hrs.
Since the quantity is 3x the time must be between 1 and 2 hours.
Cheers,
Stan H.
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