A park has frogs and crickets. Frogs eat crickets so the frog population is determined by the cricket population. When the park has \(c\) thousand crickets,  there are \(f(c)\) hundred frogs.  The cricket population changes over time and is given by \(c(t)\) thousand crickets where \(t\) is measured in weeks since the beginning of the year.  In this situation, the composition function \(f\circ g\) has input units of and output units of .

Given the two functions and , calculate (`x`) Round your final answer to two decimal places.   Desmos (click to reveal)

Consider the tables of function values below. \(t\) 1 2 3 4 5 \(f(t)\) 2 4 8 14 22 \(f\,’\,(t)\) 1 3 5 7 9   \(t\) 1 2 3 4 5 \(g(t)\) 11 13 11 8 3 \(g\,’\,(t)\) 2 0 -2 -4 -6   What is the value of \(\left(\frac{f}{g}\right)’\,(`x`)\)? Round your answer to two decimal places.   Desmos (click to reveal)

Given \(f(x)=5x^2e^{3x}\), what is the formula for \(f\,^\prime(x)\)? Note: If you want to format your answer properly, you can use the equation editor. It’s one of the “Insert” options in the menu above the answer box.

The percentage of mice with a particular genetic mutation is currently `a`% and is growing by `aprime`% per year. In a particular county there are now `c` thousand mice and this number is decreasing by `cprime` thousand mice per year.  At what rate is the number of mice in this country with the genetic mutation changing right now? Report your answer with two decimal places. (The units of your answer should be “thousand mice per year”.)   Desmos (click to reveal)

Maintenance of behavior change is best promoted by:

At a certain farm there are currently `a` acres of land growing crops, and this amount of land is decreasing by `aprime` acres per year. The crops this year will earn a profit of about `p` dollars per acre. The cost of food is rising and profits are increasing at a rate of `pprime` dollars per acre per year. At what rate is the total profit of the farm changing this year? Note: You are being asked to compute the rate of change of the total profit, the problem gives you information about the profit of just one acre of land.   Desmos (click to reveal)

Given the tables of values below: \(x\) 1 2 3 4 \(f(x)\) 4 3 2 1   \(x\) 1 2 3 4 \(g(x)\) 3 2 1 2   What is the value of \(g\circ f\) (`x`)?

Using percentages as a measure is best suited for behaviors that:

When a supervisee repeatedly fails to follow instructions, supervisors should: