Question

A bacteria population increases exponentially at a rate of r% each day.
After 32 days, the population has increased by 309%.
Find the value of r.

Answer 1

Dear Student,

◆ Answer -

r = 0.04402 %

● Explaination -

Population has increased by 309 % -

P = (100+309)/100 × P₀

P = 4.09 P₀

Bacterial population after time t is given by formula.

P = P₀.e^(rt)

4.09 P₀ = P₀.e^(32r)

4.09 = e^(32r)

Taking log on both sides -

logₑ(4.09) = 32r

1.408 = 32r

r = 0.04402 %

Hope that helps you...