Eight hundred forty nine divided by four
2 answers:
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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:
Answer:
Statement A is correct about Sam's box and whisker plot.
Step-by-step explanation:
We have been given a box plot and we are asked to find out true statement according to the box plot.
Since we know data represented by box plot is divided in four equal parts.
Upon looking at our box plot we can see that our data is symmetric. It's median is 15, which means half the math assignments have less than 15 problems and half of the math assignments have more than 15 problems.
Interquartile range represents 50% values of data and it is the difference between upper quartile and lower quartile. IQR is not affected by outliers.
Upon substituting given values from box plot we get,
From IQR we can conclude that half of the assignments contained 15 problems or fewer.Therefore, option A is the correct choice.