Question

Please answer all questions:

1)Write the formula for the updating function mt+1 = f(mt) in the following scenario, and then find the solution function mt = f(t). During a particularly dry season, the volume of water in a lake increases by 3% each day from precipitation, and then 8% of the volume of water is removed through a river. On day t0, the lake has 20,000 acre feet of water.

2)Use the solution function from the above example to determine the time it would take under these conditions for the lake’s volume to be reduced by half.

3) Identify the average, amplitude, period, and phase of the following oscillating functions.

(a) g(t) = cos(5(t + π)) − 3.

(b) h(t) = 1 ?8+6cos(2π(2t−1))?

4)The function f(x) has the following properties: f(3) = 5, f(4) = 2, and f′(3) = −2. Write the equations for the secant line of f between x = 3 and x = 4, and the tangent line at x = 3.

5) Identify the critical points and state where the function is increasing and decreasing for the function f(x)=x^3-3x. The find the derivative of f(x) and sketch it

6)Suppose a function f(x) = g(x)/h(x) . Use the following table to calculate f′(3), and write the equation of the tangent line to f at x = 3.

x	g(x)	h(x)	g′(x)	h′ (x)
2	1	2	1.5	-1
3	2	1	2	0.5
4	4.5	2	2	1

Answer 1