1. A steel drum in the shape of a right circular cylinder isrequired to have a volume of 100 cubic feet.

a. Expressthe amount A of material required to make the drum as a function of the radiosr of the cylinder.

b. How muchmaterial is required if the drums radius is 3 feet?

c. How muchmaterial is required if the drums radius is 5 feet?

d. Graph andidentify the radius that would require the least amount of material.

2. Suppose the population of species of fish (in thousands)is modeled by F(x)=x+10/0.5x^2+1, where x≥0is in years.

a. findthe equation of the horizontal asympytote.

b. Determinethe initial population,

c. Whathappens to the population of the fish as the number of years increase?

d. Interpretthe horizontal asymptote in terms of the fish population.

3. The Doppler effect is the change in pitch (frequency) ofsound from a source (s) as heard by an observer (o) when one or both are inmotion. If we assume both the source and the observer are moving in the samedirection, the relationship is f^(')=f[a]((v-v[o])/(v-v[s]))

Where: f^(‘)=perceivedpitch by the observer

F[a]=actualpitch of the source

V=speedof sound in air (assume 772.4 mph)

V[o]=speedof observer

V[s]=speedof source

Suppose that you are traveling down the road at 45mph andyou hear an ambulance (with siren) coming toward you from the rear. The actualpitch of the siren is 600 hertz (Hz).

A. Writea function f^(‘)(v[s]) that describes this scenario.

B. Iff^(‘)=620 Hz find the speed of the ambulance.

C. Graphthe function and determine using the trace function what is the pitch perceivedby the observer when the speed of the source is 80mph.