Help on algebra question

Question

during a research experiment it was found that the number of bacteria in a culture grew at a rate proportional to its size. At 10 AM there were 3000 bacteria present in the culture. At noon the number of bacteria grew to 3500. How many bacteria will there be at midnightPlease help

Answer 1

This is an exponential growth situation.

 

A(t) = A₀e^kt

 

t = hours elapsed since 10 AM

 

At noon, t = 2.

 

3500 = 3000 e^k(2)

 

k = ln(3500/3000) / 2 ≅ 0.077075 hours^-1

 

A(t) = 3000 e^{0.077075 t}

 

At midnight, t = 14.

 

A(14) = 3000 e^0.077075(14) = ?