Answer:
a).
b).
c). 6429 bacteria
Step-by-step explanation:
Population of the bacteria grows exponentially.
Therefore, growth of the bacteria will be represented by the formula
Where = Population of the bacteria after time t
= Initial population of the bacteria
k = growth constant
t = time taken for growth
Now we plug in the values in the formula
= 500
= 300
Time t = 4 hours
Now we take the natural log (ln) on both the sides
4k(lne) = ln(500) - ln(300)
4k = 6.2146 - 5.7038
4k = 0.5108
k =
a). Recursive formula for the sequence formed by the bacterial growth
Since
500 = (1 + r)300
r =
Therefore, the recursive formula will be
b). Explicit formula for the number of the bacteria will be
c). We have to calculate the number of bacteria after 24 hours
bacteria