Population growth---- help!!!?

Question

I really need help with this problem...

Population of bacteria grows at a rate proportional to the number of bacteria present at time "t". After 3hrs is it observed that 400 bacteria are present. after 10hrs 2000 bacteria are present. What was the initial number of bacteria?

thank you SO MUCH!!

Answer 1

Looking at your hr 3 time and hr 10 time the rate of bacterial growth doesnt appear to be exponential (usually the way bacterial growth problems are).  So you need to find what the rate of growth is from hour 3 to hour 10.  The rate of growth is found as follows: 2000/400 and since there are 7 hours from hour 3 to hour 10, take the 7th root: (2000/400)^(1/7)  This is the growth rate, which should be approximately 1.258498.  Now to find the initial population:  This will be (400/x)^(1/3)=1.258498;  this is the cube root of the hour 3 population divided by the initial population set equal to the growth rate.Take the cube of each side (multiply each side by 1^3).  You will get (400/x)=1.258498^3 . Solve for x. The answer should be approximately 200.  Test your answer. Take 200*1.258498^10 and you should get close to the value at hour 10, which is 2000 (off a little bit due to rounding).

Answer 2

one and a half