Find the average rate of change of the function over the given interval. y = √3x + 1; between x = 1 and x = 8 The average rate of change of y between x = 1 and x = 8 is (Simplify your answer. Type an integer or a simplified fraction.)

The amount of growth of plants in an ungrazed pasture is a function of the amount of plant biomass already present and the amount of rainfall.t For a pasture in the arid zone of Australia, the following formula gives an approximation of the growth. Y = -55.12 - 0.01535N - 0.00056N? + 3.946R Here Ris the amount of rainfall, in millimeters, over a 3-month period, Nis the plant biomass, in kilograms per hectare, at the beginning of that period, and Y is the growth, in kilograms per hectare, of the biomass over that period. (For comparison, 100 millimeters is about 3.9 inches, and 100 kilograms per hectare is about 89 pounds per acre.) Now we consider the amount of growth Y as a function of the amount of plant biomass N already present. (a) First we assume that the rainfall is 80 millimeters, so R = 80. (1) Find a formula for the growth Y as a function of the amount N of plant biomass already present. kg/ha (ii) Make a graph of Y versus N. Include biomass levels N from 0 to 800 kilograms…

A cube has an edge of 5 feet. The edge is increasing at the rate of 4 feet per minute. Express the volume of the cube as a function of m, the number of minutes elapsed. Hint:Remember that the volume of a cube is the cube (third power) of the length of a side. V (m) = feet³

The area of a square is a function of the measure, s, of a side of the square and given by  f(s) = s2.  the area (in square centimeters) of a square whose sides measure 13 centimeters.  sq cm