Answer :
Hence, the growth rate of p(t) after 4 hours is 40 bacteria per hour.
(a) The interpretation of p(2) = 186 is the population of the slowly growing bacterial colony after 2 hours is 186. Therefore, the correct interpretation is "After 2 hours, the colony has 186 bacteria in it."
b) Given that p(t) = 2t² + 24t + 130, the growth rate of p(t) after 4 hours is obtained by calculating p′(4).
Thus, p′(t) = d p(t) / dt = 4t + 24.
Substitute t = 4 in the above equation:
p′(4) = 4(4) + 24
= 16 + 24
= 40.
The growth rate of p(t) after 4 hours is 40 bacteria per hour.
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