1)The point P(2,5) and Q(3,12) lie on the parabola y=x^2+2x-3 a)Find the slope o

Question

1)The point P(2,5) and Q(3,12) lie on the parabola y=x^2+2x-3

a)Find the slope of the secant PQ.

b)Find the slope of the tangent to the parabola at P

c)Find the equation of the tangent at P

d)Graph the parabola, the secant, and the tangent

2)The annual amount of waste taken to a landfill site can be modeled by the function w(t)=110(t^2+15t+40), where w is measured in tonnes at t is the number of years since 1990. Explain the meaning of each expression in terms of the landfill site:

a)w(10)-w(5)/10-5

b)4(4.001)-w(4)/0.001

3)The ratio of surface area to volume of a cylinder of radius 7 cm is given by the function

f(h)=14pih+98pi/49pih, where h represents the height of the cylinder in cm:

Find:

a)a simpler algebraic form for this fucntion

b)the ratio of surface area to volume at a height of 4cm

c)the average rate of change as height changes from 4cm to 9cm

d)the instananeous rate of change at 9cm

4)Fluorine-20 is a radioactive substance that decays over time. At time 0, the mass of a sample of the substance is 20 g. The mass decreases to 10g after 11 s, to 5g after 22s, and to 2.5g after 33s. Compare the average rate of change over the 33-s interval with the average rate of chnage over consecutive 11-s intervals.

Explanation / Answer

a)(12-5)/(3-2)=7

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