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The infinite geometric series is converges if |r| < 1.
We have r = 0.7 < 1, therefore our infinite geometric series is converges.
The sum S of an infinite geometric series with |r| < 1 is given by the formula :
We have:
Substitute:
Answer: c. Converges, 40.
Answer:
The initial number of bacteria in the culture was 1949
Step-by-step explanation:
The relative growth rate for a certain type of bacteria population is 78% per hour.
As we know the growth of bacteria is exponential function.
where,
P is population of bacteria after n hours.
P₀ is initial population.
r is rate of growth per hour
n is number of hours
A small culture has formed and in just 5 hours the count shows to be 34,820 bacteria in the culture.
P = 34820 , n = 5 , r = 0.78
Hence, The initial number of bacteria in the culture was 1949