A population of honeybees increased at a rate of r(t) bees per week. Use midpoint rule with 6 subintervals to estimate the increase in the bee population during the first 24 weeks.

Question

anonymous · Answer

I hope one of you answers are 33

mathmale · Answer

You'll need either a table of x and y values or a function to tackle this problem.  currently it includes NO numerical data other than that the first time value is 0 weeks and the last time value is 24 weeks.  while not strictly necessary, a sketch of the time function involved would be really helpful.  

You'll need to subdivide the horizontal axis into 6 equal subintervals between 0 and 24 weeks.

You'll need to find the midpoint of each such subinterval, and then to calculate the value of r  (which represents the RATE of honeybee population) for each of the 6 midpoints.

What next?

In the end, you sum up the 6 separate rectangular areas to obtain an estimate of the honeybee population after 24 weeks.