Question

A bacteria culture has an initial population of 10,000. If it's initial population declines to 6,000 in 8 hours, what will it be at the end of 10 hours? Assume that population decreases according to the exponential model.

Answer 1

There will be `5281` bacteria after `10` hours.

Explanation:

Initial population of bacteria is `p_0 =10000 ; p_8=6000 ; t= 8` hrs.

Exponential model is `p_t= p_0*e^(kt) :. 6000= 10000*e^(k*8)` or

`e^(8*k) = 6000/10000=3/5=0.6`

Taking natural log on both sides we get `8*k ln(e) = ln (0.6) ; or 8*k ~~ -0.5108 [ln(e)=1] or k ~~ -0.5108/8 = -0.06385`

Population of bacteria after 10 hours is `p_10 = p_0*e^(k*10)` or

`p_10 = 1000*e^(-0.06385*10) =10000*e^(-0.6385) = 10000/e^(0.6385) ~~ 5281`

There will be `5281` bacteria after `10` hours. [Ans]