Exponential function

Question

A sample of  peanut butter is found to contain a concentration of 50000 bacteria per ml. Suppose that the growth of the bacterial concentration is exponential. 

A) find the exponential model for the bacterial concentration

B) if the concentration doubles every 4 hours,  how long will it take for it to reach 375000 bacteria per no?

C) estimate the concentration of bacteria atter 24 hours

Answer 1

(A)

 

Assuming the concentration doubles every T hours,

 

C(t) = C₀ (2)^t/T

 

t = hours

 

T = doubling period

 

C₀ = initial concentration = 50,000 bacteria per ml

 

(B)

 

T = 4 hours

 

375,0000 = 50,000 (2)^t/4

 

7.5 = 2^t/4

 

log7.5 = (t/4)log2

 

t = 4 log7.5 / log2 ≅ 11.63 hours

 

(C)

 

C(24) = 50,000 (2)^24/4 = ? bacteria per ml

 

You can finish from here.