Exponential Functions

Question

A bacteria culture starts with 1000 bacteria and grows at a rate proportional to its size. After 2 hours there will be 2000 bacteria.

(a) Express the population PP after tt hours as a function of t .
P(t) =________________  

(b) What will be the population after 5 hours? ______bacteria

(c) Estimate how long will it take for the population to reach 1310? Give your answer accurate to at least 2 decimal places_________

Answer 1

P = 1000*(2^t/2)

 

at t = 5 , P = 1000* 2^2.5 = 5656.854

 

1310 = 1000 * 2^t/2 => log 1.31 = (t/2) log 2

 

t = 2 * log 1.31/log 2 = .389