Libby’s family went out to dinner. The dinner bill was $95 and the family gave the server a 20% tip.
2 answers:
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Answer:
Peculiar purples would be more abundant
Step-by-step explanation:
Given that eculiar Purples and Outrageous Oranges are two different and unusual types of bacteria. Both types multiply through a mechanism in which each single bacterial cell splits into four. Time taken for one split is 12 m for I one and 10 minutes for 2nd
The function representing would be
i) for I bacteria where t is no of minutes from start.
ii) for II bacteria where t is no of minutes from start. P0 is the initial count of bacteria.
a) Here P0 =3, time t = 60 minutes.
i) I bacteria P =
ii) II bacteria P =
b) Since II is multiplying more we find that I type will be more abundant.
The difference in two hours would be
c) i) for I bacteria where t is no of minutes from start.
ii) for II bacteria where t is no of minutes from start. P0 is the initial count of bacteria.
d) At time 36 minutes we have t = 36
Peculiar purples would be
The rate may not be constant for a longer time. Hence this may not be accurate.
e) when splits into 2, we get
where P0 is initial and t = interval of time
Answer:
a) Figure attached
b) For this case we just need to see what is the value of the function when x tnd to infinity. As we can see in our original function if x goes to infinity out function tend to 1000 and thats our limiting size.
c)
And if we find the derivate when t=1 we got this:
And if we replace t=10 we got:
d)
And then:
Step-by-step explanation:
Assuming this complete problem: "A lake is stocked with 500 fish, and the population increases according to the logistic curve p(t) = 10000 / 1 + 19e^-t/5 where t is measured in months. (a) Use a graphing utility to graph the function. (b) What is the limiting size of the fish population? (c) At what rates is the fish population changing at the end of 1 month and at the end of 10 months? (d) After how many months is the population increasing most rapidly?"
Solution to the problem
We have the following function
(a) Use a graphing utility to graph the function.
If we use desmos we got the figure attached.
(b) What is the limiting size of the fish population?
For this case we just need to see what is the value of the function when x tnd to infinity. As we can see in our original function if x goes to infinity out function tend to 1000 and thats our limiting size.
(c) At what rates is the fish population changing at the end of 1 month and at the end of 10 months?
For this case we need to calculate the derivate of the function. And we need to use the derivate of a quotient and we got this:
And if we simplify we got this:
And if we simplify we got:
And if we find the derivate when t=1 we got this:
And if we replace t=10 we got:
(d) After how many months is the population increasing most rapidly?
For this case we need to find the second derivate, set equal to 0 and then solve for t. The second derivate is given by:
And if we set equal to 0 we got:
And then:
