Forest park campgrounds charges a $100 membership fee plus $35 per night. woodland campgrounds charges a $20 membership fee plus $55 per night. your friend says that if you plan to camp for four or more nights, then you should choose woodland campgrounds. is your friend correct? explain.

For 4 nights stay we can stay in any campgrounds, but for more than 4 nights we should prefer Forest park Campgrounds.

Step-by-step explanation:

Forest park Campgrounds charges a membership fees = $100

and charges per night = $35

Charges for 4 nights stay

Total charges for 4 nights = 100 + 35×4

                                       = 100 + 140

                                       = $240

Charges for 5 nights stay = 100 + 35×5

                                          = 100 + 175

                                          = $275

Woodland Campground charges a membership fees = $20

and charges per night = $55

Charges for 4 nights stay = $20 + $55×4

                                          = 20 + 220

                                          = $240

Charges for 5 nights stay = 20 + 55×5

                                           = 20 + 275

                                           = $295

Therefore, for 4 nights stay we can stay in any campgrounds because charges for both are same for 4 nights.

But for more than 4 nights we should stay in Forest park Campgrounds because Forest park charges less than other campgrounds.

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.