Answer:
Step-by-step explanation:
Given the population of an ant colony is modeled by the function
P(t) = 1,000,000/1 + 99e^-0.52t where P(t) is the population of the colony after t days. To get what q,000,000 population represents, we will substitute P = 1,000,000 into the formula and calculate t.
P(t) = 1,000,000/1 + 99e^-0.52t
1000,000= 1,000,000/1 + 99e^-0.52t
cross multiply
1,000,000 (1 + 99e^-0.52t) = 1,000,000
1 + 99e^-0.52t = 1
99e^-0.52t = =1 -1
99e^-0.52t = 0
e^-0.52t = 0
take ln of both sides;
ln(e^-0.52t ) = ln0
-0.52t = ln0
-0.52t = infinity
t = infinity.
Since t tens to infinity, this shows that 1,000,000 population is the maximum population the colony can have
Answer:
D
Step-by-step explanation:
Maximum population the colony can have
