Please help me to explain these problems.

1) Suppose that total revenue is R(x) = 50x0.5x^2 and total cost is C(x) = 10x+3 (both given in

dollars), where x represents the number of units of a product that are produced and sold. Find

the rate of change of the profit with respect to time when x = 10 units and dx/dt = 5 units per

day.

(a) $200 per day

(b) $150 per day

(c) $80 per day

(d) $50 per day

2) A ladder 25 ft long leans against a vertical wall. If the lower end is being moved away from the

wall at a rate of 6 ft/s, how fast is the height of the top changing (the answer will be a negative

rate) when the lower end is 7 ft from the wall?

(a) -6 ft/s

(b) 1.75 ft/s

(c) -1.75 ft/s

(d) -2.083 ft/s

3) For f(x) = ex, which of the following statements is false?

(a) f is negative for all x.

(b) f(x) is positive for all x.

(c) The graph of f has no points of inflection.

(d) The graph of f is increasing.

4) 10. Which of the following statements is false?

(a) ln(AB) = ln(A) + ln(B)

(b) ln(A/B) = ln(A) ln(B)

(c) e^ln(x) = x

(d) ln(x^r) = r ln(x^r1)

5) For g(x) = ln(x), which of the following statements is false?

(a) The graph of g is concave down.

(b) g(x) is positive for all x in the domain of g.

(c) The graph of g has no relative extrema.

(d) The domain of g is (0,).

6) If y = e, then dy/dx is

(a) e

(b) 0

(c) 2.718

(d) None of the above.

7) If y = ln(3), then dy/dx is

(a) 1/3

(b) 1.10

(c) 0

(d) None of the above.

8) The concentration C, in parts per million, of a medication in the body t hours after ingestion is

given by the function C(t) = 10t^2e^t, where t 0. Find the maximum value of the concentration

and the time at which it occurs.

(a) 5.4 ppm at t = 2 hr

(b) 4.61 ppm at t = 0.59 hr

(c) 2 ppm at t = 5.4 hr

(d) There is no maximum concentration.

Suppose that P0 = $1, 000 is invested in the Mandelbrot Bond Fund for which interest

is compounded continuously at 5.9% per year. That is, the balance P grows

at the rate given by

dP/dt= 0.059P.

9 ) What is the balance after 2 years?

(a) $1,125.24

(b) $1,060.78

(c) $2,121.56

10) In about how many years will an investment of $1,000 double itself?

(a) 1.22 years

(b) 3.52 years

(c) 11.75 years