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.
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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...
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